A

Adachi, Norio. 1999.
Elliptic curves: from Fermat to Weil. Pierre de Fermat mathématicien francais (Tokyo, 1998). Historia Sci. (2) 9 (1999), no. 1, 27-35.
Adler, Allan. 1997.
Eisenstein and the Jacobian varieties of Fermat curves. Rocky Mt. J. Math. 27, No.1, 1-60
abstracts: Zbl
keywords: Eisenstein, quadratic forms, elliptic functions
Alekseeva, N. B. 1989.
From the history of the theory of finite field (in Russian, English summary). Istor. Metod. Estestv. Nauk 36: 11-16.
abstracts: Zbl
Keywords: Galois, Dedekind, Dirichlet, finite field
Almkvist, Gert & Bruce, Berndt. 1988.
Gauß, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, $\pi$ and the Ladies' Diary. American Mathematical Monthly 95: 585-608.
abstracts: Zbl
Keywords: Gauß, Landen, Ramanujan, means, mathematical journals.
Antropov, A. A. 1989.
Partitioning of forms into genera and the reciprocity law in papers of L. Euler. (Russian) Vopr. Istor. Estestvozn. Tekh. 1, 56-57
abstracts: Zbl
Keywords: binary quadratic forms, genus, Gauß, reciprocity law
Antropov, A. A. 1989.
On the history of the notion of genus of binary quadratic forms (in Russian, English summary). Istor. Metod. Estestv. Nauk 36: 17-27.
abstracts: Zbl
Keywords: binary quadratic forms, genus, Gauß
Antropov, A. A. 1995.
On Euler's partition of forms into genera. Hist. Math. 22 No.2, 188-193
abstracts: Zbl
Keywords: binary quadratic forms, genus, Gauß
Aquilino, Barbara, Funk Herbert & Glaus, Beat (eds.). 1993.
Übungen zur Zahlentheorie von Adolf Hurwitz. Schriftenreihe der ETH-Bibliothek 32. Zürich, ETH-Bibliothek. 131 p.
Keywords: Hurwitz, lecture notes
B
Bachmann, Paul. 1911.
Über Gauß' zahlentheoretische Arbeiten. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse: 455-508. In überarbeiteter Form in Gauss: Werke Bd. X/2, Göttingen/Leipzig 1922, Abh. 1, 75 S.
Keywords: Gauß's Disquisitiones, congruences, quadratic reciprocity law, binary quadratic forms, cyclotomy, Gaußian sums, higher reciprocity laws, arithmetical properties of complex numbers.
Bashmakova, Isabelle. 1949.
Obosnovanie teorii delimosti v trudach E.I. Zolotareva (in Russian). Istoriko-matematiceskie issledovanija 2: 233-351.
Keywords: Zolotarev, ideal numbers, divisor theory, p-adic numbers, number theory in Russia, Markov, Woronoj, cubic fields, Grave, Ott Julinowitsch Schmidt, Tchebotarev, Delaunay, Tartakowsky, local methods.
Bashmakova, Isabelle. 1960.
Le théorème fondamental de l'algèbre et la construction des corps algébriques. Archives internationales d'histoire des sciences 16: 211-222.
Keywords: Gauß, Kronecker, fundamental theorem of algebra, decomposition field
Bashmakova, Isabelle. 1971.
Les méthodes locales de E.I. Zolotareff. In XIIe Congrès International d'Histoire des Sciences. Paris 1968. Actes. Tome IV: Histoire des mathématiques et de la mécanique. Paris, Blanchard: 11-15.
Keywords: Zolotarev, p-adic numbers, local methods.
Begehr, Heinrich; Koch, Helmut; Kramer, Jürg; Schappacher, Norbert & Thiele, Ernst-Jochen (eds.). 1998.
Mathematics in Berlin. Berlin, Birkhäuser. 200p. ISBN 3-7643-5943-9
abstracts: Zbl
Keywords: Berlin, Crelle, Dirichlet, Jacobi, Eisenstein, Kronecker, Kummer, E. Schmidt, Hasse, mathematical institutions, mathematical journals.
Bell, Eric Temple. 1944.
Gauß and the Early Development of Algebraic Numbers. National Mathematics Magazine 18: 188-204, 219-233.
abstracts: Zbl
Keywords: Gauß's problem solving, factorization of algebraic numbers, Disquisitiones Arithmeticae, binary quadratic forms, Dedekind, complex multiplication, Eisenstein, reciprocity, congruences, Hilbert.
Bell, Eric Temple. 1945.
The Development of Mathematics. 2nd Edition. New York/London, McGraw-Hill.
abstracts: Zbl
Keywords: Disquisitiones Arithmeticae, diophantine equations, Pell's equation, quadratic forms, Gauß, Eisenstein, Siegel, congruences, applications of analysis.
Benis-Sinaceur, Hourya. 1984. see Sinaceur 1984.
Bergé, Anne-Marie and Martinet, Jacques. 1986.
Sur la constante d' Hermite (note historique). Séminaire de théorie des nombres de Bordeaux 1, exposé 8.
abstracts: Zbl
Keywords: Hermite, Korkine, Zolotareff, Voronoi, Minkowski, Blichfeldt, extreme forms, perfect forms, lattice packings, eutactic forms, Hermite's constant.
Binder, Christa & Hlawka, Edmund. 1986.
Über die Entwicklung der Theorie der Gleichverteilung in den Jahren 1909 bis 1919. Archive for the History of Exact Sciences 36: 197-249.
abstracts: Zbl
Keywords: uniformly distributed sequence, Bohl, Weyl, F. Bernstein, Hardy, Littlewood, Sierpinski.
Biermann, Kurt-R. 1959.
Johann Peter Gustav Lejeune Dirichlet. Dokumente für sein Leben und Wirken. Zum 100. Todestag. Abhandlungen der Deutschen Akademie der Wissenschaften zu Berlin. Klasse für Mathematik, Physik und Technik 2. 96 p.
abstracts: Zbl
Keywords: Dirichlet.
Biermann, Kurt-R. 1960.
Dirichletiana. Monatsberichte der Deutschen Akademie der Wissenschaften zu Berlin. Mitteilungen aus Mathematik, Naturwissenschaft, Medizin und Technik 2: 386-389.
Keywords: Dirichlet.
Biermann, Kurt-R. 1964.
Gotthold Eisenstein. Die wichtigsten Daten seines Lebens und Wirkens. Journal für die reine und angewandte Mathematik 214: 19-30.
abstracts: Zbl
Keywords: Eisenstein (biographical data).
Biermann, Kurt-R. 1966.
Richard Dedekind im Urteil der Berliner Akademie. Forschungen und Fortschritte 40: 301-302.
abstracts: Zbl
Keywords: Kronecker on Dedekind's number theoretical work.
Biermann, Kurt-R. 1971.
Zu Dirichlets geplantem Nachruf auf Gauß. Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin 8 (1): 9-12.
abstracts: Zbl
Keywords: Dirichlet's obituary of Gauß, Dirichlet on Riemann and Dedekind.
Biermann, Kurt-R. 1988.
Die Mathematik und ihre Dozenten an der Berliner Universität 1810-1933. Berlin, Akademie Verlag.[ISBN 3-05-500402-7]
abstracts: Zbl
Biermann, Kurt-R. 1997.
Spiel mit Zahlen: Carl Friedrich Gauß als Codemaker. Kultur und Technik 1997!1): 39-41.
Keywords: Gauß, codes, applications of number theory.
Bölling, Reinhard. 1997.
Kummer vor der Erfindung der ``idealen complexen Zahlen'': das Jahr 1844. Acta historica Leopoldina 27: 145-157.
Keywords: ideal numbers, Kummer, prime factorization of cyclotomic numbers.
Boniface, Jacqueline. 1999.
Kronecker et le concept de nombre. La Gazette des mathématiciens 81.
abstracts: Zbl
Keywords: concept of number, Kronecker.
Boniface, Jacqueline.
Hilbert et la notion d'existence en mathématiques. Mathesis. Paris, Vrin.
Keywords: Hilbert, Dedekind, Cantor Kronecker, mathematical objects, existence in mathematics, constructivity, philosophy of mathematics.
Bordogna, Francesca. 1996.
Interpreting the Ideal: Embedding Ideal Numbers in the Mathematical Programs of Kummer, Dedekind and Klein. Preprint 47 of the Max Planck Institut für Wissenschaftsgeschichte. 46 pages + 8.
Keywords: ideal numbers, lattices, algebraic numbers, Kummer, Dedekind, Klein, geometry and number theory, arithmetization, mathematical concepts, mathematical programs.
Brezinski, Claude. 1991.
History of Continued Fractions and Padé Approximants. Berlin, Springer. [ISBN 3-540-15286-5]
abstracts: Zbl
Keywords: continued fractions.
Brigaglia, Aldo & Scimone, Aldo. 1998.
Algebra and Number Theory. In The Italian Mathematics after Unification. The Years between World Wars I and II, edited by Simonetta di Sieno et al. Milano, Marcos y Marcos: 505-567. [ISBN 88-7168-153-3/hbk]
abstracts: Zbl
Keywords: number theory in Italy.
Brüning, Jochen & Ferus, Dirk & Siegmund-Schultze, Reinhard. 1998.
Terror and Exile. Persecution and Expulsion of Mathematicians from Berlin between 1933 and 1945. Berlin, DMV.
Keywords: pictures, Berlin mathematics, Bohr, Hardy, Schur, Remak, E. Schmidt, Vahlen, Weyl, mathematics and politics.
C
Cartier, Pièrre. 1993.
Des nombres premiers à la géometrie algébrique (une brève histoire de la fonction zeta), Cah. Semin. Hist. Math., 2. Ser. 3, 51-77
abstract: Zbl
keywords: zeta function, Weil conjectures
Cassels, J.W.S. 1973.
Louis Joel Mordell 1888-1972 (Elected F.R.S. 1924). Biographical Memoirs of Fellows of the Royal Society 19 : 493-520.
Keywords: Mordell, number theory in Great-Britain, diophantine equations, approximations.
Cassels, J.W.S. 1974.
L. J. Mordell (1888 - 1972). Bulletin of the London Mathematical Society 6: 69-96.
abstracts: Zbl
Keywords: Mordell, number theory in Great Britain, diophantine equations, approximations.
Cassels, J. W. S. 1986.
Mordell's finite basis theorem revisited. Mathematical Proceedings of the Cambridge Philosophical society 100: 31-41.
abstracts: Zbl
Keywords: Mordell, Weil, elliptic curves, diophantine equations, conjecture, Mordell-Weil theorem.
Clarke, F. W.; Everitt, W. N.; Littlejohn, L. L.; Vorster, S. J. R. 1999
H. J. S. Smith and the Fermat two squares theorem. Amer. Math. Monthly 106 (1999), no. 7, 652-665
Collison, Marie Joan. 1977.
The Origins of the Cubic and Biquadratic Reciprocity Laws. Archive for History of Exact Sciences 16: 63-69.
abstracts: Zbl
Keywords: Gauß, Eisenstein, Jacobi, priority questions, reciprocity laws
Conte, Alberto & Giacardi, Livia (ed.) 1991.
Angela Genocchi e i suoi interlocutori scientifici. Contributi dall' epistolario. Torino, Deputazione Subalpina di Storia Patria. 395p.
Keywords: Genocchi
Corry, Leo. 1996.
Modern Algebra and the Rise of Mathematical Structures. Science Networks 17. Basel/Boston/Berlin, Birkhäuser. 460p. ISBN 3-7643-5311-2
abstracts: Zbl
Keywords: Dedekind, Noether, Van der Waerden, Hilbert, Fraenkel, Ore, Bourbaki, structures, ideals, algebraic number fields, rings, images
del Corso, I. 1995.
On Kronecker's use of indeterminate coefficients. (English)w Rend. Semin. Mat., Torino 53, No.3, 261-275
abstracts: Zbl
Keywords: Dedekind domain, divisors
Cox, David A. 1984. The arithmetic-geometric mean of Gauss. Enseign. Math. 30, 275-330
abstracts: Zbl
Keywords: arithmetic-geometric mean; elliptic integrals; Jacobian theta functions; congruence subgroups; Gauss
D
Dauben, Joseph (ed.). 1981.
Mathematical Perspectives. Essays on Mathematics and Its Historical Development. Presented to Professor Dr. Kurt-Reinhard Biermann on the Occasion of His 60th Birthday. New York, Academic Press. 272p.
abstracts: Zbl
Damerow, Peter. 1996.
Number as a second order concept. Science in Context 9: 139-149.
Keywords: number concept in number theory, Dedekind, cognitive aspects, education
Décaillot, Anne-Marie. 1998.
L'arithméticien Edouard Lucas (1842-1891): théorie et instrumentation. Revue d'histoire des mathématiques 4(2): 191-236.
abstracts: Zbl
Keywords: Lucas, prime numbers, Fermat's little theorem, Mersenne numbers, primality tests, elementary methods, number theory in France, mathematical societies, recurrent series, computations, experimentation, mathematical instruments.
Dickson, Leonard. 1916/17.
Fermat's last theorem and the origin and nature of the theory of algebraic numbers. Annals of Mathematics. Second Series 18: 161-187.
abstracts: FdM
Keywords: Fermat's Last Theorem, prime factorization of algebraic numbers.
Dieudonné, Jean. 1974.
Cours de géométrie algébrique. Tome I. Paris, PUF. [English translation: 1985. History of Algebraic Geometry. An Outline of the Historical Development of Algebraic Geometry. Monterrey, Wadsworth.]
abstracts: Zbl(English ed.)
Keywords: algebraic geometry and number theory, Kronecker, Dedekind, Weber, function field, resultant.
Dieudonné, Jean (ed.). 1978.
Abrégé d'histoire des mathématiques 1700-1900. 2 volumes. Paris, Hermann. [German translation: 1985. Wiesbaden/Braunschweig, Vieweg].
abstracts: Zbl (2nd ed.) Zbl (German ed.)
Dirichlet, P. G. L. 1999.
Lectures on Number Theory. Supplements by R. Dedekind. Translated by John Stillwell. American Mathematical Society, London Mathematical Society. 275 pages. ISBN 0-8218-2017-6
Abstract: English translation of the 1863 classic. Zbl
Keywords: Lejeune Dirichlet, number theory, binary quadratic forms, class number formula, L-series
Drake, Reuben Carbert. 1976.
A Developmental Study of Ideal Theory. Ph.D. diss. Washington, The American University.
Keywords: ideals in algebraic number theory, in algebraic geometry, modern algebra, ideals in analysis and topology.
can be ordered at UMI
Dugac, Pierre. 1978.
Richard Dedekind et les fondements des mathématiques. Paris, Vrin.
abstracts: Zbl
Keywords: Dedekind, number theory and the foundations of mathematics, Cantor, influence of Dedekind, biographical information (archive material).
Dvornicich, Roberto. 2000.
The influence of David Hilbert in number theory. (Italian) In: The ideas of David Hilbert (Italian) Catania, 1999. Matematiche (Catania) 55, suppl. 1, 75-91
E
Echeverria, Javier. 1992.
Observations, problems and conjectures in number theory - the historyof the prime number theorem. In The Space of Mathematics. Philosophical, epistemological and historical explorations, edited by Javier Echeverria, Andoni Iberra and Thomas Mormann. Grundlagen der Kommunikation und Kognition. Berlin, De Gruyter: 230-252.
abstracts: Zbl
Keywords: philosophy of number theory, prime number theorem, repartition of primes, tables, empirical formulas, proofs, experimentation, Pafnuti Chebyshev.
Echeverria, Javier. 1996.
Empirical Methods in Mathematics. A Case-Study: Goldbach's Conjecture. In Spanish Studies in the Philosophy of Science, edited by Gonzalo Munévar. Dordrecht, Boston & London, Kluwer: 19-55.
Keywords: empirical methods, Goldbach's Conjecture, tables, conjectures, additive number theory
Edwards, Harold M. 1974.
Riemann's Zeta Function. Academic Press, London and New York. 315 pages. ISBN 0-12-232750-0
abstracts: Zbl
Keywords: Riemann, Riemann hypothesis, prime number theorem, zeta function, Hadamard, H. von Mangoldt, de la Vallée Poussin, Hardy, Lindelöf, Euler-Maclaurin summation, Riemann-Siegel formula
Edwards, Harold M. 1975.
The Background of Kummer's Proof of Fermat's Last Theorem for Regular Primes. Archive for History of Exact Sciences 14: 219-236
abstracts: Zbl
Keywords: Kummer, Fermat's last theorem, ideal theory, unique factorization, cyclotomy
Edwards, Harold M. 1977.
Postscript to ``The Background of Kummer's Proof ...'' Archive for History of Exact Sciences 17: 381-394
abstracts: Zbl
Keywords: Kummer, Fermat's last theorem, ideal theory, unique factorization, cyclotomy
Edwards, Harold M. 1977.
Fermat's Last Theorem; A Genetic Introduction to Algebraic Number Theory. Graduate Texts in Mathematics. New York, Springer Verlag. 410 pages. ISBN 0-387-90230-9, 3-540-90230-9.
abstracts: Zbl
Keywords: Fermat's last theorem, elementary number theory, algebraic number theory, binary quadratic forms, class number formula, cyclotomy, Fermat, Euler, Ernst Kummer, Germain
Edwards, Harold M. 1977.
Review of: Ernst Eduard Kummer. Collected Papers. Historia Mathematica 4: 475-478.
Keywords: Kummer
Edwards, Harold M. 1978.
On the Kronecker Nachlass. Historia Mathematica 5: 419-426.
Keywords: Kronecker, Hensel, Hasse
Edwards, Harold M. 1980.
The Genesis of Ideal Theory. Archive for History of Exact Sciences 23: 321-378.
abstracts: Zbl
Keywords: Kummer, Dedekind, Kronecker, ideal theory, algebraic integer, divisor theory
Edwards, Harold M. 1982.
Kummer, Eisenstein, and Higher Reciprocity Laws. In Number Theory Related to Fermat's Last Theorem, edited by Neal Koblitz. Progress in Mathematics 26. Birkhäuser, Boston-Basel-Stuttgart: 31-43.
abstracts: Zbl
Keywords: Kummer, Eisenstein, higher reciprocity laws, Legendre symbols, Jacobi symbols, tables
Edwards, Harold M. 1983.
Dedekind's Invention of Ideals. Bulletin of the London Mathematical Society 15: 8-17.
abstracts: Zbl
Keywords: Dedekind, ideal theory, completed infinites
Edwards, Harold M. 1983.
Euler and Quadratic Reciprocity. Mathematics Magazine 56: 285-291.
abstracts: Zbl
Keywords: Euler, law of quadratic reciprocity
Edwards, Harold M. 1984.
Galois Theory. Graduate Texts in Mathematics. New York, Springer-Verlag. 152 pages. ISBN 0-387-90980-X, 3-540-90980-X
abstracts: Zbl
Keywords: Galois, Galois theory, Galois group, cyclotomy, resolvent, algebraic extension, algebraic equations, solvability
Edwards, Harold M. 1987.
An Appreciation of Kronecker. The Mathematical Intelligencer 9(1): 28-35.
abstracts: Zbl
Keywords: Leopold Kronecker, Kronecker-Weber theorem
Edwards, Harold M. 1987.
Dedekind's invention of ideals. Studies in the history of mathematics, MAA Stud. Math. 26, 8-20
abstracts: Zbl
Keywords: Kronecker; Kummer; Lejeune-Dirichlet; Riemann
Edwards, Harold M. 1992.
Mathematical Ideas, Ideals, and Ideology. The Mathematical Intelligencer 14(2): 6-19.
abstracts: Zbl
Keywords: Dedekind, Kummer, Kronecker, set theory, algebraic number theory, ideal theory, divisor theory, foundations of mathematics
Edwards, Harold M. 1988.
Kronecker's Place in History. History and Philosophy of Modern Mathematics., edited by Philip Kitcher and William Aspray. Minnesota Studies inthe Philosophy of Science XI. Minneapolis, University of Minnesota Press: 139-144.
Keywords: Kronecker, foundations of mathematics
Edwards, Harold M. 1990.
Divisor theory. Birkhäuser Verlag. [ISBN 0-8176-3448-7]
abstracts: Zbl
Keywords: divisors; Kronecker; algebraic number field; Dedekind ideals; differentials; function field
Edwards, Harold M. 1990.
A Note on Galois Theory. Archive for History of Exact Sciences 41: 163-169.
abstracts: Zbl
Keywords: Galois, algebraic equations, splitting field
Edwards, Harold M. 1992.
Kronecker's Arithmetical Theory of Algebraic Quantities. Jahresberichte der Deutsche Mathematiker Vereinigung 94: 130-139.
abstracts: Zbl
Keywords: Kronecker, general arithmetic
Edwards, Harold M. 1995.
Kronecker on the Foundations of Mathematics. In From Dedekind to Gödel. Essays on the Development of the Foundations of Mathematics, edited by Jaakko Hintikka. Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science 251. Dordrecht, Kluwer: 45-52.
Keywords: Kronecker, foundations of mathematics, set theory, completed infinites
Edwards, Harold, Neumann, Olaf & Purkert, Walter. 1982.
Dedekinds ``Bunte Bemerkungen" zu Kroneckers ``Grundzüge''. Archive for History of Exact Sciences 27 : 49-85.
abstracts: Zbl
Keywords: Dedekind, Kronecker's Grundzüge, Weber, ideal theory, arithmetical theory of algebraic quantities.
Edwards, Harold. 1998.
Kummer and Kronecker. In Mathematics in Berlin, edited by Heinrich Begehr et al. Berlin, Birkhäuser: 61-69.
abstracts: Zbl
El'natanov, B. A. 1984.
The Development of the Sieve Method. Dushanbé.
El'natanov, B. A. 1983.
Short outline of the history of the development of the sieve of Eratosthenes. (Russian) Istor.-Mat. Issled. 27, 238-259
abstracts: Zbl
Keywords: Euler; Gauss; Legendre; Liouville; Dedekind; de Jonguieres; Lipschitz, Riemann; de Polignak; Chebyshev; Sludskij; Spatschinskij; Dirichlet; Lebesgue; Bunjakowskij; Porezkij; Lebon; Morehead; Dines; Sylvester; Meissel; Rogel; Paci; Kronecker; Mertens; Romanowskij; Merlin; Buchstab
F
Fenster, Della. 1999.
Leonard Dickson's History of the Thoery of Numbers: an historical study with mathematical implications. Revue d'histoire des mathématiques 5(2): 159-179.
abstracts: Zbl
Keywords: Dickson, history of number theory.
Ferreirós, José. 1991.
El Nacimiento de la teoria de conjuntos. Madrid, Ediciones de la Universitad Autónoma. [English revised translation: 1999. Labyrinth of Thoughts. A History of Set Theory and its Role in Modern Mathematics. Basel/Boston/Berlin, Birkhäuser.]
Keywords: philosophy of number theory, Dedekind, ideal theory, ideal numbers, algebraic number theory.
1982. Festschrift der Braunschweigischen Wissenschaftlichen Gesellschaft und der Technischen Universität Carolo Wilhelmina zu Braunschweig zur 150. Wiederkehr des Geburtstages von Richard Dedekind. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 33. Göttingen, Goltze. 268 p.
abstracts: Zbl
Keywords: Dedekind.
Flanders, Harley. 1960.
The meaning of the form calculus in classical ideal theory. Transactions of the American Mathematical Society 95: 92-100.
abstracts: Zbl
Keywords: foundation of ideal theory, Kronecker, local methods, theory of forms.
Folkerts, Menso & Neumann, Olaf (eds.). 2002.
Der Briefwechsel zwischen Kummer und Reuschle. Ein Beitrag zur Geschichte der algebraischen Zahlentheorie. München, Institut für Geschichte der Naturwissenschaften. 218 p.
Keywords: correspondences, Kummer, Reuschle, algebraic number theory
Frei, Günther. 1979.
On the Development of the Genus of Quadratic Forms. Les Annales des sciences mathématiques du Québec 3 (1): 5-62.
abstracts: Zbl
Keywords: quadratic forms, genus, quadratic reciprocity law.
Frei, Günther. 1984.
Les nombres convenables de Leonhard Euler. Publ. Math. Fac. Sci. Besancon, Theor. Nombres 1983/1984, 58 p.
abstracts: Zbl
Keywords: numeri idonei; convenient numbers; class number; quadratic forms; quadratic fields
Frei, Günther. 1985a.
Leonhard Euler's convenient numbers. Math. Intell. 7, 55-58, 64
abstracts: Zbl
Keywords: numeri idonei; convenient numbers; class number; quadratic forms; quadratic fields
Frei, Günther. 1985b.
Helmut Hasse (1898-1979). A biographical sketch dealing with Hasse's fundamental contributions to mathematics, with explicit references to the relevant mathematical literature. Expo. Math. 3, 55-69
abstracts: Zbl
Frei, Günther. 1989.
Heinrich Weber and the Emergence of Class Field Theory. In The History of Modern Mathematics, edited by David E. Rowe and John McCleary . Vol. I: Ideas and Their Reception. Boston, Academic Press: 425-450.
Keywords: class-field theory, Weber, Hilbert.
Frei, Günther. 1994.
The Reciprocity Law from Euler to Eisenstein. In The Intersection of History and Mathematics, edited by Sasaki Chikira, Sugiuru Mitsuo & Joseph Dauben. Science Networks 15. Basel/Boston/Berlin, Birkhäuser: 67-90.
abstracts: Zbl
Keywords: reciprocity laws, Eisenstein, Euler, Gauß, Jacobi.
Frei, Günther. 1998a.
Zur Geschichte des Crelleschen Journals. Journal für die reine und angewandte Mathematik 500: 1-4.
abstracts: Zbl
Keywords: mathematical journals, Crelle, Kronecker, Borchardt
Frei, Günther. 1998b.
Helmut Hasse und seine Arbeiten im Crelleschen Journal. Journal für die reine und angewandte Mathematik 500: 15-21.
abstracts: Zbl
Keywords: Hasse, mathematical journals, local-global principal, quadratic forms, reciprocity law,complex multiplication, function fields, algebras
Frei, Günther. 2001.
How Hasse was led to the theory of quadratic forms, the local-global principle, the theory of the norm residue symbol, the reciprocity laws, and to class field theory. In: Class field theory - its centenary and prospect (Tokyo, 1998), 31--62, Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, 2001
Fuchs, Werner. 1980.
Zur Lehre von den Kongruenzen bei C. F. Gauss. I. Mitt., Gauss-Ges. Gött. 17, 14-29
abstracts: Zbl
Keywords: residue classes; Fermat's theorem; Euler phi-function; linear congruences; calendar; Gaussian Easter formula
Fuchs, Werner. 1981.
Zur Lehre von den Kongruenzen bei C. F. Gauss. II. Mitt., Gauss-Ges. Gött. 18, 49-62
abstracts: Zbl
Keywords: primitive roots; indices; linear congruences; periodic decimal fractions
Fuchs, Werner. 1982.
Zur Lehre von den Kongruenzen bei C. F. Gauss. III. Mitt., Gauss-Ges. Gött. 19, 63-78
abstracts: Zbl
Keywords: quadratic reciprocity law; congruences; Legendre symbol;
G
Gana, Francesco 1986.
Dio e l'uomo nella matematica di Kronecker. Historia Mathematica 13: 255-276.
abstracts: Zbl
Keywords: philosophy of number theory, Kronecker, set theory, Dedekind, operations with algebraic numbers, arithmetization.
Gana, Francesco. 1988.
L'eliminatione dell' infinito nella matematica di Kronecker. In Storia degli studi sui fundamneti della matematica e connessi sviluppi interdisciplinari. Vol. II. Roma, Luciani: 140-157.
Keywords: Kronecker, infinity
Gendrihson, N.N. 1974.
Gauss' Hypothese ueber den Aufbau der Einheiten in Kreisteilungskoerpern. (Russian) Trudy 13 mezdunarod. Kongr. Istor. Nauki, Moskva 1971; Istor. Mat. Meh.abstracts: Zbl
Gispert, Hélène. 1991.
La France mathématique. La Société mathématique de France (1870-1914). Suivi de cinq études par Rudolf Bkouche, Christian Gilain, Christian Houzel, Jean-Pierre Kahane, Martin Zerner. Cahiers d'histoire et de philosophie des sciences 34. Paris, Société fran�aise d'histoire des sciences et des techniques et Société mathématique de France. 423 p. ISBN: 2-905746-05-X an 2-85629-012-4.
abstracts: Zbl
Keywords: Société mathématique de France, number theory in France, quantitative data, theses, Hermite, Poincaré, Dirichlet series, algebraic geometry.
Gispert, Hélène. 1999.
Réseaux mathématiques en France dans les débuts de la Troisième République. Archives internationales d'histoire des sciences 49: 122-149.
Keywords: number theory in France, Société mathématique de France, Association fran�aise pour l'avancement des sciences.
Gispert, Hélène & Tobies, Renate. 1996.
A comparative study of the French and German mathematical societies before 1914. In L'Europe mathématique: Histoires, mythes, identités. Mathematical Europe: History, myth, identity, edited by Catherine Goldstein, Jeremy Gray et Jim Ritter. Paris, Editions de la Maison des sciences de l'homme: 407-430.
abstracts: Zbl
Keywords: mathematical societies, international comparison, number theory in France, number theory in Germany
Goldstein, Catherine. 1989.
Le métier des nombres au 17e et 19e siècles. &EACUTE;léments d'Histoire des Sciences, edited by Michel Serres. Paris, Bordas: 274-295. [English translation: 1995. A History of Scientific Thought, Oxford et Cambridge (MA), Blackwell: 344-371].
Keywords: Fermat, Kummer, Fermat Last Theorem, professions, textual practices, institutions, pure mathematics, international comparison, number theory and philosophy.
Goldstein, Catherine. 1993.
Descente infinie et analyse diophantienne: programmes de travail et mise en oeuvre chez Fermat, Levi, Mordell et Weil. Cahier du Séminaire d'Histoire et de Philosophie des Mathématiques (2) 3: 25-49.
abstracts: Zbl
Keywords: Mordell, Weil, Fermat, infinite descent, elliptic curves, diophantine equations, Poincaré, B. Levi, mathematical programs, classifications, heights.
Goldstein, Catherine. 1993.
Sur l'histoire du théorème de Mordell-Weil. Publications du séminaire de théorie des nombres de Caen 93/94: 1-8.
Keywords: Mordell, Weil, elliptic curves, diophantine equations, historiography of number theory, history of mathematics and mathematics.
Goldstein, Catherine. 1994.
La théorie des nombres dans les Notes aux comptes rendus de l'Académie des sciences (1870-1914): un premier examen. Rivista di Storia della scienza (II) 2 (2) : 137-160
Keywords: number theory in France, classifications, networks and communities, journals, elementary methods, theory of forms, analytic methods, reception of ideal theory in France, statistics on number theory, comparison between France and Germany.
Goldstein, Catherine. 1995.
Un théorème de Fermat et ses lecteurs. Histoires de science. Saint-Denis, Presses Universitaires de Vincennes. 229p. ISBN 2-910381-10-2
abstracts: Zbl
Keywords: congruent numbers, elliptic curves, diophantine equations, Fermat, Dickson, Weil, historiography of number theory, textual practices, social history of mathematics.
Goldstein, Catherine, Gray, Jeremy & Ritter, Jim (eds.). 1996.
L'Europe mathématique. Mythes, histoires, identités - Mathematical Europe. Myth, history, identity, Paris, Editions de la Maison des sciences de l'homme. 575p. ISBN 2-7351-0685-3
abstracts: Zbl
Goldstein, Catherine. 1999.
Sur la question des méthodes quantitatives en histoire des mathématiques: le cas de la théorie des nombres en France (1870-1914). Acta historiae rerum naturalium nec non technicarum (New series 3) 28: 187-214.
Keywords: Hermite, Lucas, Poincaré, Pépin, de Jonquières, Humbert, Jordan, classification, social history of mathematics, quantitative data, international comparison, number theory in France.
Gray, Jeremy. 1984.
A Commentary on Gauß's Mathematical Diary, 1796-1814, with an English Translation. Expositiones Mathematicae 2: 97-130
abstracts: Zbl
Keywords: Gauß, diary.
Gray, Jeremy. 1990.
Herausbildung von strukturellen Grundkonzepten der Algebra im 19. Jahrhundert. In Geschichte der Algebra. eine Einführung, edited by Erhard Scholz. Mannheim/Wien/Zürich, BI-Wissenschaftsverlag: 293-323.
Keywords: Kummer, Dedekind, binary quadratic forms, ideal numbers, ideal theory.
Goldman, Jay R. 1998.
The Queen of Mathematics; A Historically Motivated Guide to Number Theory. A. K. Peters, Wellesley, Massachusetts. 525 pages. ISBN 1-56881-006-7
Abstract: A textbook covering a variety of topics in elementary and intermediate number theory with extensive historical references.
Keywords: number theory, history, Gauß, Disquisitiones Arithmeticae
Grell, H. 1968.
David Hilbert. Gesamtpersönlichkeit und algebraisch-zahlentheoretisches Werk. Mitteilungen der Mathematischen Gesellschaft der DDR 2: 1-46.
Keywords: Hilbert.
Gruber, Peter Manfred. 1990.
Zur Geschichte der Konvexgeometrie und der Geometrie der Zahlen. In Ein Jahrhundert Mathematik 1890-1990. Festschrift zum Jubiläum der DMV, edited by Gerd Fischer, Friedrich Hirzebruch, Winfried Scharlau und Willi Törnig. Dokumente zur Geschichte der Mathematik 6. Braunschweig, Vieweg: 421-455.
abstracts: Zbl
Keywords:
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Kurt Hensels entscheidender Anstoß zur Entdeckung des Lokal-Global-Prinzips. Journal für die reine und angewandte Mathematik 209: 3-4.
abstracts: Zbl
Keywords: local methods, Hensel, quadratic forms.
Hasse, Helmut. 1967.
History of Class Field Theory. In Algebraic Number Theory, edited by J.W. S. Cassels and A. Fröhlich. London/New York, Academic Press: 266-279.
Haubrich, Ralf. 1992.
Zur Entstehung algebraischen Zahlentheorie Richard Dedekinds. Göttingen, Universität Göttingen. 234p.
abstracts: Zbl
Keywords: ideals, Gauß, Dedekind, Dirichlet, Eisenstein, Kummer, Riemann, Bachmann, Meyer, reciprocity, extensions, factorization, algebraic number theory.
Haubrich, Ralf. 1998.
Frobenius, Schur and the Berlin Algebraic Tradition. In Mathematics in Berlin, edited by Heinrich Begehr et al. Berlin, Birkhäuser: 83-96.
abstracts: Zbl
Keywords: Frobenius, Schur, Berlin.
Heath, Thomas 1910.
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abstracts: Zbl
Houzel, Christian.1992
La préhistoire des conjectures de Weil. In Development of Mathematics 1900-1950, edited by Jean-Paul Pier. Basel/Boston/Berlin, Birkhäuser: 385-413.
abstracts: Zbl
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Cahit Arf's contribution to algebraic number theory and related fields. Turkish J. Math. 22 (1998), no. 1, 1-14.
Ischebeck, Friedrich. 1993.
Primzahlfragen und ihre Geschichte. Math. Semesterber. 40 (1993), no. 2, 121-132
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Helmut Hasse, Hermann Ludwig Schmid and their students in Berlin. In Mathematics in Berlin, edited by Heinrich Begehr et al. Berlin, Birkhäuser: 143-149.
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Zum Beweis von C. F. Gauß für die Irreduzibilität des p-ten Kreisteilungspolynoms. Historia Mathematica 11: 131-141.
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An afterthought of Gauss on cyclotomy. Proceedings of the 2nd Gauss symposium. Conference A: Mathematics and theoretical physics, Munich, Germany, August 2-7, 1993. Berlin: Walter de Gruyter. Symposia Gaussiana. 147-150
abstracts: Zbl
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Séries de Fourier, séries de Taylor, séries de Dirichlet; un aper�u de l'importance des travaux des mathématiciens fran�ais dans la période 1880-1910. In La France mathématique, edited by Hélène Gispert. Cahiers d'histoire et de philosophie des sciences 34. Paris, Société fran�aise d'histoire des sciences et des techniques et Société mathématique de France: 277-297.
Keywords: Dirichlet series, analytical number theory, Stieltjes, Riemann hypothesis, Hadamard, prime number theorem.
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How Fermat's Last Theorem was proved. Pierre de Fermat mathématicien francais (Tokyo, 1998). Historia Sci. (2) 9 (1999), no. 1, 49-56
Kersten, Ina. 2000.
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Kiss, E. 1995.
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abstracts: Zbl
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Kiss, Elemer. 1999.
Mathematical gems from the Bolyai chests. Janos Bolyai's discoveries in number theory and algebra as recently deciphered from his manuscripts. Translated by Aniko Csirmaz and Gabor Olah. (English) Budapest: Akademiai Kiado. Budapest: TypoTEX Ltd. Electronical Publishing. 200 p. ISBN 963-05-7563-9/hbk
abstracts: Zbl
Kiss, Elemer. 1999.
Notes on Janos Bolyai's researches in number theory. Hist. Math. 26, No.1, 68-76
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Kleiner, Israel. 1995.
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abstracts: Zbl
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Kleiner, Israel. 1996.
The genesis of the abstract ring concept. Am. Math. Monthly 103, No.5, 417-424
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Kleiner, Israel. 1998.
From Numbers to Rings: The Early History of Ring Theory. Elemente der Mathematik 53: 18-35.
abstracts: Zbl
Keywords: ring theory, ideal theory, algebraic geometry, invariant theory, algebras, binary quadratic forms, Dedekind, Fermat's Last Theorem, reciprocity laws, Kummer, ideal numbers.
Koblitz, Neal (ed.). 1982.
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abstracts: Zbl
Koch, Helmut. 1981.
Über das Leben und Werk Johann Peter Gustav Lejeune Dirichlets. Zu seinem 175. Geburtstag. Sitzungsberichte der Akademie der Wissenschaften der DDR. Mathematik - Naturwissenschaft - Technik 17N: 1-12.
abstracts: Zbl
Keywords: Dirichlet.
Koch, Helmut. 1985.
Die Rolle der Zetafunktionen in der Zahlentheorie von Euler bis zur Gegenwart. Abh. Akad. Wiss. DDR, Abt. Math. Naturwiss. Tech. 1985, Nr. N1, 120-124
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Koch, Helmut. 1998.
Gustav Peter Lejeune-Dirichlet. In Mathematics in Berlin, edited by Heinrich Begehr et al. Berlin, Birkhäuser: 33-39.
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Keywords: Dirichlet; Fourier series; primes in arithmetic progression; unit theorem
Kolmogorov, Andrei N.& Yushkevich, Adolf-Andrei P. (eds.). 1978.
Matematika XIX. veka. Matematischeskaya logika, algebra, teoryia chisel, teoryia veroyatnostei. Moskva, Nauka. [English translation: 1992. Mathematics of the 19th Century. Mathematical Logic, Algebra, Number Theory, Probability Theory. Basel/Boston/Berlin, Birkhäuser.]
abstracts: Zbl
Konen, H. 1901.
Geschichte der Gleichung t²-Du². Leipzig, Hirzel. 132 p.
Keywords: Pell's equation, binary quadratic forms, continued fractions.
Knobloch, Eberhard, Pieper, Herbert & Pulte, Helmut. 1995.
``... das Wesen der reinen Mathematik verherrlichen''. Mathematische Semesterberichte 42 (2): 99-132.
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Die Zolotareffsche Begründung der algebraischen Zahlentheorie in moderner Sicht. Unveröffentliche Staatsexamensarbeit, Universität Hamburg.
Lang, Serge. 1995a.
Some history of the Shimura-Taniyama conjecture. Notices Amer. Math. Soc. 42 (1995), no. 11, 1301-1307.
Lang, Serge. 1995b.
Mordell's review, Siegel's letter to Mordell, Diophantine geometry, and 20th century mathematics. Gaz. Math. No. 63, (1995), 17-36. Notices Amer. Math. Soc. 42 (1995), no. 3, 339-350.
Lavrinenko, Tatiana 2002
Solving an indeterminate third degree equation in rational numbers. Sylvester and Lucas Rev. Hist. Math. 8, No.1, 67-111
Laubenbacher, Reinhard & Pengelley, David. 1999.
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abstracts: Zbl
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Lehti, Raimo. 1978.
Disquisitiones arithmeticae of Gauss. II: Transformation theory of binary quadratic forms. (Finnish) Arkhimedes 30, 177-202
abstracts: Zbl
keywords: binary quadratic forms, disquisitiones arithmeticae
Lehti, Raimo. 1981.
The Disquisitiones Arithmeticae of Gauss. III: The composition of binary quadratic forms and its connection with group theory. (Finnish) Arkhimedes 33, 12-38
abstracts: Zbl
Keywords: disquisitiones arithmeticae of Gauss; binary quadratic forms; connection with group theory
Lemmermeyer, Franz. 2000.
Reciprocity laws. From Euler to Eisenstein. Springer monographs in mathematics. Berlin/New Yor/Paris, Springer. 487 p. ISBN 3-540-66957-4
abstracts: Zbl
Keywords: reciprocity laws
Lemmermeyer, Franz & Schappacher, Norbert. 1998.
Introduction to The Theory of Algebraic Number Fields, by David Hilbert. Translated by Iain Adamson. Berlin, Springer: xxiii-xxxvi.
Lepka, Karel. 1995.
Matyas Lerch's work in number theory. Brno, Masaryk University of Science. 78p.
abstracts: Zbl
Keywords: quadratic residues, Lerch, class number of quadratic forms
Llorente, Pascual. 1984.
Number theory in the nineteenth century. (Catalan) In: The development of mathematics in the nineteenth century, 73--90, Arx. Sec. Ci�n., LXXV, Inst. Estudis Cat., Barcelona, 1984.
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Weyls Kritik an Dedekinds Zahlbegriff. Dialectica 46: 141-149.
Keywords: Weyl, Dedekind, number concept
Marion, Mathieu. 1995.
Kronecker's `safe haven of real mathematics'. In Québec studies in the philosophy of science. Part I: Logic, Mathematics, Physics and History of Science, edited by Mathieu Marion and Robert S. Cohen. Dordrecht/Boston/London, Kluwer: 189-215.
Keywords: Kronecker, philosophy of mathematics, algebraic number theory, function fields, Dedekind, Hilbert, Kronecker's Jugendtraum.
Matiyasevich, Yuri V. 1993.
Hilbert's Tenth Problem. Cambridge, MA - London: MIT Press.
abstracts: Zbl
Maurin, Krzysztof. 1997.
The Riemann legacy. Riemannian ideas in mathematics and physics Kluwer Academic Publishers. 717 p. ISBN 0-7923-4636-X/hbk]
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Mehrtens, Herbert. 1979a.
Die Entstehung der Verbandstheorie. arbor scientiarum. Beiträge zur Wissenschaftsgeschichte. Reihe A: Abhandlungen 6. Hildesheim, Gerstenberg. 363 p.
abstracts: Zbl
Keywords: Dedekind, ideal theory, module theory.
Mehrtens, Herbert. 1979b.
Das Skelett der modernen Algebra. Zur Bildung mathematischer Begriffe bei Richard Dedekind. In Zur Entstehung neuer Denk- und Arbeitsrichtungen in der Naturwissenschaft, edited by Christoph Scriba. Göttingen, Vandenhoeck & Ruprecht: 25-43.
Keywords: foundations of mathematics, methodology of mathematics, Dedekind, ideal theory.
Mehrtens, Herbert. 1990.
Moderne Sprache Mathematik. Frankfurt, Suhrkamp. 640 p. ISBN 3-518-58067-1
Merzbach, Uta. 1981.
An Early Version of Gauß's Disquisitiones Arithmeticae. In Mathematical Perspectives. Essays on Mathematics and Its Historical Development. Presented to Professor Dr.Kurt-Reinhard Biermann on the Occasion of His 60th Birthday. edited by Joseph Dauben. New York, Academic Press: 167-177.
abstracts: Zbl
Keywords: Gauß's Disquisitiones Arithmeticae.
Merzbach, Uta. 1984.
Carl Friedrich Gauß. A Bibliography. Wilmington, Scholarly Resources. 551 p. ISBN 0-8420-2169-8.
abstracts: Zbl
Keywords: Gauß.
Merzbach, Uta. 1992.
Robert Remak and the Estimation of Units and Regulators. In Amphora. Festschrift für Hans Wussing zu seinem 65. Geburtstag, edited by Serge� Demidov, Menso Folkerts, David E. Rowe and Christpoh Scriba. Berlin, Birkhäuser: 481-522.
abstracts: Zbl
Keywords: Remak, algebraic units, regulators, algebraic number fields.
Miyake, Katsuya. 1989.
A note on the arithmetic background to Frobenius' theory of group characters. Expositiones Mathematicae 7: 347-358.
abstracts: Zbl
Keywords: reciprocity laws, density theorems, Frobenius, L-series, characters, representation theory, Dedekind, binary quadratic forms.
Miyake, Katsuya. 1994.
The Establishment of the Takagi-Artin Class Field Theory. In The Intersection of History and Mathematics, edited by Sasaki Chikira, Sugiuru Mitsuo & Joseph Dauben. Science Networks 15. Basel/Boston/Berlin, Birkhäuser: 109-128.
abstracts: Zbl
Keywords: class field theory, Kronecker, Weber, abelian fields, complex multiplication, Hilbert, Furtwängler, Dedekind, Frobenius, Artin's reciprocity law, Takagi, Hecke.
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Narkiewicz, Wladyslaw. 1986.
Classical Problems in Number Theory. Monografie Matematyczne 62. Warszawa, Polish Scientific Publishers. 363p. ISBN 83-01-05931-1
abstracts: Zbl
Keywords: Mersenne numbers, perfect numbers, Artin's conjecture, Waring's theorem, binary quadratic forms
Narkiewicz, Wladyslaw. 1990.
Elementary and Analytic Theory of Algebraic Numbers. Second Edition, Substantially Revised and Extended. - Berlin et al., Springer; Warszawa, PWN--Polish Scientific Publishers. 746p.
abstracts: Zbl
Keywords: numerous historiographical remarks.
Narkiewicz, Wladyslaw. 1990.
Mathematics at Breslau University during the time of Kummer. (Polish) Wiadom. Mat. 28, 195-203
abstracts: Zbl
Keywords: Kummer,
Narkiewicz, Wladyslaw. 2000.
The development of prime number thoery. From Euclid to Hardy and Littlewood. Berlin, Springer. 448p. ISBN 3-540-66289-8.
abstracts: Zbl
Keywords: analytic number theory, prime numbers, Dirichlet, Chebyshev, Riemann, Zeta-function.
Neumann, Olaf. 1972.
``Vorwort''. In Two papers on number theory by : L. J. Mordell. VEB Deutscher Verlag der Wissenschaften : 5-8.
Neumann, Olaf. 1978.
Über einige Tagebuchnotizen von C. F. Gauß (Zur Entstehung der Kreisteilungstheorie). In Festakt und Tagung aus Anlaß des 200. Geburtstages von C. F. Gauß, edited by Hans Sachs. Abhandlungen der Akademie der Wissenschaften der DDR. Abteilung Mathematik, Naturwissenschaft, Technik 3 N: 141-150.
Keywords: cyclotomy, Gauß, Disquisitiones Arithmeticae, Gaußian sums, cyclotomic fields.
Neumann, Olaf. 1979.
Anmerkungen zur 2. und folg. Auflagen von C. F. Gauß: Mathematisches Tagebuch 1796-1814. Ostwalds Klassiker Bd. 256. Leipzig, Ostwald.
Keywords: Gauß, diary
Neumann, Olaf. 1979.
Bemerkungen aus heutiger Sicht über Gauß' Beiträge zu Zahlentheorie, Algebra und Funktionentheorie. NTM - Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin 16(2): 22-39.
abstracts: Zbl
Keywords: Gauß, quadratic reciprocity law, representation of numbers, binary quadratic forms, composition of binary quadratic forms.
Neumann, Olaf. 1980.
Zur Genesis der algebraischen Zahlentheorie. Bemerkungen aus heutiger Sicht über Gauß' Beiträge zu Zahlentheorie, Algebra und Funktionentheorie (Fortsetzung). NTM - Schriftenreihe 17 (1): 32-48 (2. Teil); 17 (2): 38-58 (3. Teil).
abstracts: Zbl (II), Zbl (III)
Keywords: cyclotomy, quadratic fields, Gaußian sums, Jacobi sums, biquadratic reciprocity, cyclotomic fields, ideal numbers, Kronecker.
Neumann, Olaf. 1981a.
Über die Anstöße zu Kummers Schöpfung der ``idealen complexen Zahlen''. In: Mathematical Perspectives. Essays on Mathematics and Its Historical Development. Presented to Professor Dr.Kurt-Reinhard Biermann on the Occasion of His 60th Birthday, edited by Joseph Dauben. New York, Academic Press: 179-199.
abstracts:Zbl
Keywords: Kummer, ideal numbers, Hensel, Fermat's Last Theorem, Kronecker, Gaußian sums.
Neumann, Olaf. 1981b.
Two Proofs of the Kronecker-Weber Theorem ``According to Kronecker, and Weber''. Journal für die reine und angewandte Mathematik 323: 105-126.
abstracts: Zbl
Keywords: Theorem of Kronecker-Weber, class field theory, abelian fields, proofs.
Neumann, Olaf. 1985.
Annotationen zu: W. et F. Ellison: Théorie des nombres. In Geschichte der Mathematik 1700 -1900, edited by Jean Dieudonné (German translation of Dieudonné 1978). Braunschweig/Wiesbaden/Berlin, Vieweg: 345-351.
Neumann, Olaf. 1987.
Gottlob Frege als Mathematiker in seiner Zeit. Alma mater Jenensis. Studien zur Hochschul- und Wissenschaftsgeschichte 4: 71-81.
Neumann, Olaf. 1990.
Biographien Dirichlet, Hermite, Legendre, Minkowski, Winogradow. In Lexikon bedeutender Mathematiker, edited by Siegfried Gottwald, Hans-Joachim Ilgauds und Karl-Heinz Schlote. Leipzig, Bibliographisches Institut.
Neumann, Olaf. 1991.
Zum Verhältnis von Mathematik und Physik. In Mathematik und Wirklichkeit, edited by Ulrich Röseberg. Berlin, Akademie-Verlag: 99-111.
Neumann, Olaf. 1997a.
Vorlesungsnachschriften zu Dirichlet-Dedekind-Kummerschen Themen - verfaßt von Paul Bachmann (1837-1920). Acta historica Leopoldina 27: 319-323.
Keywords: Bachmann, Dedekind, lecture notes
Neumann, Olaf. 1997b.
Die Entwicklung der Galoistheorie zwischen Arithmetik und Topologie (1850-1960). Archive for History of Exact Sciences 50 (3-4): 291-329.
abstracts: Zbl
Keywords: Dedekind, Kronecker, normal fields, function fields.
Neumann, Olaf. 1997c.
Gottlob Frege als Mathematiker in seiner Zeit. Kritisches Jahrbuch der Philosophie 2: 104-110.
Keywords: Frege
Neumann, Olaf. 1997d.
Carl Gustav Reuschle (1812-1875) - ein Stuttgarter Gymnasialprofessor für Mathematik, Physik und Geographie. (In Zusammenarbeit mit Menso Folkerts) 8 p. to appear in: Bericht Tagung Geschichte der Mathematik, Calw 1997
Neumann, Olaf. 1998.
Leopold Kronecker (1823-1891). 11 S. to appear in: Bericht Symposion ``Schlesische Beiträge zur Entwicklung der Wissenschaften''. Gerhard-Möbus-Institut für Schlesienforschung an der Universität Würzburg e. V. 1998.
Neumann, Olaf. 1999.
Was sollen und was sind Divisoren? Math. Semesterberichte 48 (2002), 139-192.
Neumann, Olaf, 2002.
C.F. Gauss: Disquisitiones Arithmeticae. in: Landmark Writings in Western Mathematics, 1640-1940 (I. Grattan-Guinness ed.)
Neumann, Olaf & and Purkert, Walter. 1981.
Richard Dedekind -- zum 150. Geburtstag. Mitteilungen der Mathematischen Gesellschaft der DDR 2/4: 84-110.
Keywords: Dedekind, genesis of ideal theory, Dedekind's zeta-function.
Neumann, Olaf & Purkert, Walter. 1989.
Richard Dedekind. In Biographien bedeutender Mathematiker, edited by Hans Wussing und Wolfgang Arnold. 4. edition. Berlin, Volk und Wissen: 443-457.
Keywords: Dedekind
Niederreiter, Harald. 1982.
Richard Dedekind and the development of the theory of finite fields. In Festschrift der Braunschweigischen Wissenschaftlichen Gesellschaft und der Technischen Universität Carolo Wilhelmina zu Braunschweig zur 150. Wiederkehr des Geburtstages von Richard Dedekind. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 33. Göttingen, Goltze : 183-187.
abstracts: Zbl
Keywords: Dedekind, congruences, higher congruences, finite fields.
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abstracts: Zbl
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Ozigova, E.P. 1966.
Egor Ivanovic Zolotarev. 1847-1878 (Russian), Nauka, Moskow, Leningrad 1966, 144 pp.
abstracts: Zbl
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Ozigova, E.P. 1972.
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abstracts: Zbl
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abstracts: Zbl
Keywords: Hecke, L-series, Dirichlet, primes in arithmetic progressions, complex multiplication, Gauß, class field theory, modular forms, automorphic forms, abelian varieties, Shimura, Taniyama, Langlands.
Piazza, Paola. 1998.
Zolotarev's foundation of algebraic number theory. Thesis, University of Messina.
Piazza, Paola. 1999.
Egor Ivanovich Zolotarev and the theory of ideal numbers for algebraic number fields. I, Studies in the History of Modern Mathematics IV, edited by Umberto Bottazzini. Palermo, Circolo Matematico di Palermo: 123-149.
abstracts: MR
Keywords: Zolotarev, ideal numbers, local methods, number theory in Russia.
Piazza, Paola. 2000.
Zolotarev's foundations in the theory of algebraic numbers. (Italian), Boll. Unione Mat. Ital., Mat. Soc. Cult. (8) 3 Suppl., 169-172
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Pieper, Herbert. 1978.
Variationen über ein zahlentheoretisches Thema von Carl Friedrich Gauß. With a foreword by Hans Reichardt. Wissenschaft und Kultur 33. Basel/Boston: Birkhäuser. 183 pp. ISBN: 3-7643-0959-8
Pieper, Herbert. 1998.
Carl Gustav Jacob Jacobi. In Mathematics in Berlin, edited by Heinrich Begehr et al. Berlin, Birkhäuser: 41-48.
abstracts: Zbl
Pieper, Herbert (ed.). 1987.
Briefwechsel zwischen Alexander von Humboldt und C. G. Jacob Jacobi. Edited and with an introduction by Herbert Pieper. Beiträge zur Alexander-von-Humboldt-Forschung 11. Berlin, Akademie-Verlag. 312 pp. ISBN: 3-05-000240-9
abstracts: Zbl
Pieper, Herbert. 1988a.
Urteile C. G. J. Jacobis über den Mathematiker E. E. Kummer. NTM 25 (1): 23-36.
abstracts: Zbl
Keywords: number theory; elliptic integrals; convergent series
Pieper. Herbert. 1996.
Die Eulersche Identität - eine Brücke zwischen Analysis, Arithmetik und Kombinatorik. Mitteilungen der DMV 43-49.
Pieper, Herbert. 1997.
Über Legendres Versuche, das quadratische Reziprozitätsgesetz zu beweisen. Natur, Mathematik und Geschichte. Acta historica Leopoldina 27: 223-237.
Pieper, Herbert. 1998.
Korrespondenz Adrien-Marie Legendre - Carl Gustav Jacob Jacobi. Reprint of ``Correspondance mathématique entre Legendre et Jacobi'' (1875) with German translation by E. Knobloch and B. Mai. Edited, with commentaries and an essay by Herbert Pieper. Teubner-Archiv zur Mathematik 19. Stuttgart, Teubner. 245 pp. ISBN 3-8154-2128-4
abstracts: Zbl
Pieper, Herbert & Tobies, Renate. 1988.
Zum Verhältnis deutscher Mathematiker des 19. Jahrhunderts zur Geschichte ihrer Wissenschaft. Mitteillungen der Mathematischen Gesellschaft der DDR 3-4: 55-71.
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On number theory and Kustaa Inkeri. Number theory (Turku, 1999), 281-292, de Gruyter, Berlin, 2001.
Purkert, Walter. 1973.
Zur Genesis des abstrakten Körperbegriffs. NTM. Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin 10(1): 23-37; 10(2): 8-20.
abstracts: Zbl(1st part), Zbl(2nd part)
Keywords: Gauß, Dirichlet, Kummer, congruences, Kronecker's arithmetical theory of algebraic quantities, Dedekind's algebraic number theory, Weber.
Purkert, Walter. 1976.
Ein Manuskript Dedekinds über Galois-Theorie. NTM. Zeitschrift für Geschichte der Naturwissenschaften, Technik und Medizin 13 (2): 1-16.
abstracts: Zbl
Keywords: Dedekind's Nachlaß, Galois Theory.
Purkert, Walter. 1989.
Leopold Kronecker. In Biographien bedeutender Mathematiker, edited by Hans Wussing und Wolfgang Arnold. 4. edition. Berlin, Volk und Wissen: 426-440.
Keywords: Kronecker.
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The mathematical heritage of C. F. Gauß. A Collection of Papers in Memory of C. F. Gauß. Singapore, World Scientific. 902 p.
abstracts: Zbl
Ree, David. 1995.
Figures of Thought. Londond/New York, Routledge. 183 p. ISBN: 0-415-08146-7
Keywords: Gauß, Dedekind, Kronecker, perception of mathematics, textual practices, views on numbers, Weil, arithmetic algebraic geometry, Grothendieck, generality
Reich, Karin. 1996.
Frankreich und Gauß, Gauß und Frankreich; Ein Beitrag zu den deutsch-französischen Wissenschaftsbeziehungen in den ersten Jahrzehnten des 19. Jahrhunderts. Berichte zur Wissenschaftsgeschichte 19(1): 19-34
abstracts: Zbl
Keywords: international relationships, translations, exchanges, Gauß's reception in France.
Reich, Karin. 2000.
Die Entdeckung und frühe Rezeption der Konstruierbarkeit des regelmässigen 17-Ecks und dessen geometrische Konstruktion durch Johannes Erchinger (1825). In Mathesis. Festchrift zum siebzigsten Geburtstag von Matthias Schramm, edited by Rüdiger Thiele. Berlin-Diepholz, GNT-Verlag: 101-118.
abstracts: Zbl
Keywords: regular 17-gon, rule and compass construction, reception of Disquisitiones, cyclotomy
Reichardt, Hans (ed.). 1957.
C.F. Gauß. Gedenkband anlässlich des 100. Todestages am 23. Februar 1955. Leipzig, Teubner. 251 p.
Keywords: Gauß.
Reichardt, Hans (ed.). 1963.
Bericht von der Dirichlet-Tagung. Schriftenreihe der Institute für Mathematik bei der Deutschen Akademie der Wissenschaften zu Berlin 13. Berlin, Akademie-Verlag. 82 p.
Keywords: Dirichlet, Fermat's Last Theorem, primes in arithmetic progressions, L-series, class number formulae, unit theorem, composition of forms.
Ribenboim, Paulo. 1982.
The Work of Kummer on Fermat's Last Theorem. In Number Theory Related to Fermat's Last Theorem, edited by Neal Koblitz. Progress in Mathematics 26. Birkhäuser, Boston-Basel-Stuttgart: 1-29.
Keywords: Kummer (biographical information), Fermat's Last Theorem, cyclotomic fields, regular primes, class number of cyclotomic fields, Bernoulli numbers, Jacobi sums.
Ribenboim, Paulo. 1990.
Gauss and the class number problem. In: Proceedings of the International Symposium on Mathematics and Theoretical Physics (Guaruj�, 1989), 3-63, Sympos. Gaussiana Ser. A Math. Theoret. Phys., 1, Inst. Gaussianum, Toronto, ON,
keywords: Gauss, disquisitiones arithmeticae, binary quadratic forms
Rieger, Georg Johann. 1957.
Die Zahlentheorie bei C. F. Gauß. In C. F. Gauß. Gedenkband anlässlich des 100. Todestages am 23. Februar 1955, edited by Hans Reichardt. Leipzig, Teubner: 37-77.
Keywords: Gauß, Disquisitiones Arithmeticae, congruences, quadratic reciprocity, binary quadratic forms, genus theory, reduction theory, ternary quadratic forms, Dirichlet, cyclotomy, Gaußian sums, higher reciprocity laws, arithmetic of algebraic numbers, Kronecker, continued fractions, prime number theorem, L-series.
Rohrbach, Hans. 1998.
Helmut Hasse and Crelle's Journal. Journal für die reine und angewandte Mathematik 500: 5-13.
abstracts: Zbl
Keywords: Hasse, Hensel, mathematical journals, interwar period.
Roquette, Peter (ed.). 1987.
Erich Hecke. Analysis und Zahlentheorie. Vorlesung Hamburg 1920.. Dokumente zur Geschichte der Mathematik 3. Braunschweig/Wiesbaden, Vieweg. 234p. ISBN 3-528-08997-0
abstracts: Zbl
Keywords: Hecke, zeta-functions, L-series, cyclotomic extensions, reciprocity law, complex multiplication
Roquette, P. 1989.
Über die algebraisch-zahlentheoretischen Arbeiten von Max Deuring. Jahresbericht der DMV 91, 109-125.
abstracts: Zbl
Roquette, Peter. 1998.
Zur Geschichte der Zahlentheorie in den dreißiger Jahren. Die Entstehung der Riemannschen Vermutung für Kurven und ihres Beweises im elliptischen Fall. Mathematische Semesterberichte 45, 1-38.
abstracts: Zbl
Rowe, David. 1988.
Gauß, Dirichlet and the law of biquadratic reciprocity. Mathematical Intelligencer 10(2): 13-25.
abstracts: Zbl
Keywords: Gauß, Dirichlet, biquadratic reciprocity.
Rowe, David. 1989.
Klein, Hilbert and the Göttigen Mathematical Tradition. Osiris 5:186-213.
abstracts: Zbl
Rowe, David. 1994.
The Philosophical Views of Klein and Hilbert. In The Intersection of History and Mathematics, edited by Sasaki Chikira, Sugiuru Mitsuo & Joseph Dauben. Science Networks 15. Basel/Boston/Berlin, Birkhäuser: 187-202.
abstracts: Zbl
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Sampson, J.H. 1990.
Sophie Germain and the theory of numbers. Arch. Hist. Exact Sci. 41, No.2, 157-161
abstracts: Zbl
Keywords: Fermat's last theorem; number theory
Schappacher, Norbert. 1990.
Développement de la loi de groupe sur une cubique. In Séminaire de théorie des nombres de Paris 1988-1989, edited by Catherine Goldstein. Progress in Mathematics 91. Boston, Basel & Berlin, Birkhäuser: 159-184.
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Schappacher, Norbert. 1997.
Some milestones of lemniscatomy. In Algebraic Geometry. Proceedings of the Bilkent summer school, Ankara, Turkey, August 1995, edited by Sinan Sertoez. Lecture Notes in Pure and Applied Mathematics 193. New York, Marcel Dekker: 257-290.
abstracts: Zbl
Keywords: complex multiplication, lemniscate, Eisenstein, Kronecker's Jugendtraum.
Schappacher, Norbert. 1998a.
Gotthold Eisenstein. In Mathematics in Berlin, edited by Heinrich Begehr et al. Berlin, Birkhäuser: 55-60.
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Schappacher, Norbert. 1998b.
On the History of Hilbert's Twelfth Problem. A Comedy of Errors. In Matériaux pour l'histoire des mathématiques au XXe siècle. Actes du colloque � la mémoire de Jean Dieudonné (Nice, 1996). Séminaires et congrès 3. Paris, Société mathématique de France: 243-273
abstracts: Zbl
Keywords: Kronecker, Hilbert, Weber, Hilbert problems, Kronecker-Weber theorem, Kronecker's Jugendtraum, modular functions, modular forms, elliptic curves, complex multiplication, class-field theory, geometry and number theory, change of framework, proofs, role of errors, interpretation of a theorem.
Schappacher, Norbert & Schoof, René. 1996.
Beppo Levi and the arithmetic of elliptic curves. Mathematical Intelligencer 18: 57-69
abstracts: Zbl
Schappacher, Norbert & Volkert, Klaus. 1997.
Heinrich Weber; un mathématicien � Strasbourg, 1895-1913. L'Ouvert 89: 1-18. To be reproduced in Sciences et cultures -- Les trois universités de Strasbourg 1872-1945.
Scharlau, Winfried (ed.). 1981.
Richard Dedekind 1831-1931. Eine Würdigung zu seinem 150. Geburtstag.. Braunschweig/Wiesbaden, Vieweg. 146 p.
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Keywords: Dedekind.
Scharlau, Winfried. 1982a.
Zu Dirichlets geplantem Bericht über den Gauß-Nachlaß. NTM. Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin 19 (2): 27-29.
abstracts: Zbl
Keywords: Dirichlet's obituary of Gauß, Dedekind's Nachlaß.
Scharlau, Winfried. 1982b.
Unveröffentliche algebraische Arbeiten Richard Dedekinds aus seiner Göttinger Zeit 1855-1858. Archive for History of Exact Sciences 23: 335-355.
abstracts: Zbl
Scharlau, Winfried & Opolka, Hans. 1985.
From Fermat to Minkowski. Lectures on theTheory of Numbers and Its Historical Development. Undergraduate Texts in Mathematics. New York, Springer. 184 p.
abstracts: Zbl
Keywords: Gauß, Dirichlet, binary quadratic forms, reduction theory, Pell's equation, continued fractions, modules and forms, Minkowski.
Scharlau, Winfried. 1986.
Zur Entstehung der Algebraischen Zahlentheorie -- Bericht eines Augenzeugen. Archive History of Exact Sciences 36, 63-74.
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Keywords: Lipschitz, Dirichlet, reciprocity laws, Jacobi sums, Kummer, cyclotomy.
Scharlau, Winfried. 2000.
On the history of the algebraic theory of quadratic forms. In Quadratic Forms and their Applications, edited by Eva Bayer-Fluckiger et al. Contemporary Mathematics 272. Providence R.I., AMS: 229-259.
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Schinzel, Andrzej. 1993.
The History of Number Theory in Poland in the Years 1851-1950 (Polish). Annales de la Société mathématique de Pologne II 30(1): 19-50.
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Keywords: Mertens, Sierpinski, Walfisz, Lubelski, number theory in Poland
Schinzel, Andrzej. 1997.
One hundred years of the prime number theorem. (Polish) Ann. Soc. Math. Pol. Ser. II, Wiad. Mat. 33, 91-98
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Schinzel, Andrzej. 2001.
Number theory in the "Disquisitiones arithmeticae". (Polish) in Mathematics in the Gauss era (Polish) (Zielona Góra, 2000), 137--141, WSP, Zielona Góra, 2001
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Schneider, Ivo (ed.). 1981.
Carl Friedrich Gauß (1777-1855). Sammelband von Beiträgen zum 200. Geburtstag. München, Minverva Publikation. 245 p.
abstracts: Zbl
Schneider, Th(eodor). 1993.
Das Werk C. L. Siegels in der Zahlentheorie. Jahresbericht der Deutschen Mathematiker-Vereinigung 85: 147-157.
Keywords: Siegel (biographical information), additive number theory, functional equation of Dedekind zeta-function, diophantine approximation, transcendal numbers, analytical theory of quadratic forms.
Scholz, Erhard. 1982.
Herbart's influence on Bernhard Riemann. Historia Mathematica 9: 413-440.
abstracts: Zbl
Keywords: Riemann, Bildungsphilosophie, epistemology, unity of science
Scholz, Erhard (ed.). 1990.
Geschichte der Algebra. Eine Einführung. Lehrbücher und Monographien zur Didaktik der Mathematik 16. Mannheim/Wien/Zürich, BI-Wissenschaftsverlag.
abstracts: Zbl
Schuppener, Georg. 1994.
Geschichte der Zeta-Funktion von Oresme bis Poisson. Deutsche Hochschulschriften 533. Egelsbach, Hänsel-Hohenhausen. 196p. ISBN: 3-89349-533-9
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Schwermer, Joachim. 1986.
Über Reziprozitätsgesetze in der Zahlentheorie. In Arithmetik und Geometrie. 4 Vorlesungen, edited by Horst Knörrer et al. Mathematische Miniaturen 3. Basel/Boston/Stuttgart, Birkhäuser: 29-69.
Keywords: reciprocity laws, L-series, Gauß, Kummer, Eisenstein, Hilbert, Takagi.
Schwermer, Joachim. 1991.
Räumliche Anschauung und Minima positiv definiter quadratischer Formen. Zur Habilitation von Hermann Minkowski 1887 in Bonn. Jahresbericht der Deutschen Mathematiker-Vereinigung 93: 49-105.
Keywords: Minkowski, positiv definite quadratic forms, lattices, reduction theory, Gauß's Disquisitiones Arithmeticae, Dirichlet, geometry and numbers, Hermite, Jacobi.
Scimone, Aldo. 2001.
The first two hundred years of the Disquisitiones arithmeticae (1801--2001). (Italian) Lett. Mat. Pristem Scriba, Christoph. 1970.
Zur Entwicklung der additiven Zahlentheorie von Fermat bis Jacobi. Jahresbericht der Deutschen Mathematiker-Vereiningung 72: 122-142.
abstracts: Zbl
Keywords: additive number theory, Jacobi, Legendre, Gauß, analytic methods, elliptic functions, series, infinite products
Scriba, Christoph. 1977.
Zum 200. Geburtstag von Carl Friedrich Gauß. In Beiträge zum Mathematikunterricht 1977. Hannover, Dortmund, Darmstadt & Berlin, Hermann Schroedel: 9 p.
Keywords: symmetry in Gauß' work, cyclotomic equations, arithmetico-geometric means
Scriba, Christpoh (ed.). 1979.
Disciplinae novae. Zur Entstehung neuer Denk- und Arbeitsrichtungen in der Naturwissenschaft. Festschrift zum 90.Geburtstag von Hans Schimanek. Göttingen, Vandenhoeck & Ruprecht 1979.
abstracts: Zbl
Scriba, Christoph. 1980.
Viggo Brun in Memoriam (1885-1978). Historia Mathematica 7: 1-6.
abstracts: Zbl
Keywords: Brun, Goldbach conjecture, sieve methods, continued fractions, Thue, Selberg, number theory in Norway, history of number theory.
Scriba, Christoph. 1984.
Zur Geschichte der Bestimmung rationaler Punkte auf elliptischen Kurven. Das Problem von Beha-Eddin Amuli Berichte aus den Sitzungen der Joachim Jungius-Gesellschat der Wissenschaften e. V., Hamburg 1(6). 52 p. ISBN 3-525-86204.0
Keywords: diophantine equations; arithmetic of elliptic curves; Jacobi; Nesselman; Lucas; Mordell; Poincaré.
Scriba, Christoph. 1985.
Zur Erinnerung an Viggo Brun. Mitteilungen der mathematischen Gesellschaft in Hamburg 11 (3): 271-290.
Keywords: Brun, sieve methods, Goldbach conjecture, twin prime numbers, music and number theory.
Scriba, Christoph. 1992.
In Memoriam Clas-Olof Selenius (1922-1991). Historia Mathematica 19: 325-327.
Keywords: Selenius, continued fractions, number theory in Sweden
Schwarz, Wolfgang. 1990.
Geschichte der analytischen Zahlentheorie seit 1890. In Ein Jahrhundert Mathematik 1890-1990. Festschrift zum Jubilaeum der DMV. Friedr. Vieweg, Dok. Gesch. Math. 6, 741-780 [ISBN 3-528-06326-2]
abstracts: Zbl
keywordds: analytic number theory; distribution of prime numbers; sieve methods; Dirichlet L-series; uniform distribution; diophantine approximation;
Schwarz, Wolfgang. 1994.
Some remarks on the History of the Prime Number Theorem from 1896 to 1960. In Development of Mathematics 1900-1950, edited by Jean-Paul Pier. Basel/Boston/Berlin, Birkhäuser: 565-616.
abstracts: Zbl
Serre, Jean-Pierre. 1993.
Smith, Minkowski et l'Académie des sciences. Avec des notes de Norbert Schappacher. Gazette des mathématiciens 56: 3-9. [Translated into German with annotations by Norbert Schappacher: 1993. Mitteilungen der deutschen Mathematiker-Vereinigung 2: 4-7.
abstracts: Zbl
Keywords: Minkowski, Smith, Hermite, prizes, quadratic forms, international relationships
Shields, Allen. 1989.
Lejeune-Dirichlet and the Birth of Analytic Number Theory 1837-1839. Mathematical Intelligencer 11(4): 7-11.
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Keywords: Dirichlet, Kummer, Klein, Mendelsohn connection, analytic number theory, Crelle
Siegel, Carl Ludwig. 1932.
Über Riemanns Nachlaß zur analytischen Zahlentheorie. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung B: Studien, 2, 45-80. (= In Gesammelte Abhandlungen, Vol. 1, Springer-Verlag, Berlin and New York, 1966.)
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Keywords: Riemann-Siegel formula, Riemann hypothesis, Riemann zeta function
Sinaceur, Hourya. 1984.
De D. Hilbert à E. Artin: Les differents aspects du dix-septieme problème et les filiations conceptuelles de la théorie des corps réels clos. Archive for the History of Exact Sciences 29: 267-286.
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Sinaceur, Hourya. 1990.
Corps et modèles. Mathesis. Paris, Vrin. 496 p. ISBN: 2-7116-1038-1.
Keywords: Sturm theorem, Hermite, Sylvester, Cauchy, Witt, quadratic forms, Artin-Schreier, real closed fields, arithmetization, algebirzation, logic and number theory, Tarski, model theory.
Skula, Ladislav. 1994.
Some historical aspects of the Fermat problem. (Czech) Pokroky Mat. Fyz. Astron. 39, No.6, 318-330
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Keywords: Fermat's last theorem; infinite descent; ideal numbers; irregular primes; Kummer; Bernoulli numbers; Fermat quotients
Slavutskii, I. Sh. 1995.
Staudt and arithmetical properties of Bernoulli numbers. Historia Scientiarum II 5(1): 69-74.
abstracts: Zbl
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Slavutskii, I. Sh. 1990.
Studies in the history of arithmetical prorperties of Bernoulli numbers (Staudt, Kummer, Voronoi) (in Russian). Istoriko-matematiceskie issledovanija 32/33: 158-181.
abstracts: Zbl
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Soublin, Jean-Pierre. 1984.
Préhistoire des idéaux. Cahiers du Séminaire d'Histoire des Mathématiques: 13-20.
abstracts: Zbl
Keywords: ideal numbers, Kummer, unique factorization theorem in cyclotomic fields.
Springer, T. A. 1978.
The theory of quadratic forms in the Disquisitiones Arithmeticae. In Carl Friedrich Gauß. 1777-1855. Four lectures on his life and work, edited by A. F. Monna. Communications of the Mathematical Institute 7. Utrecht, Rijksuniversiteit Utrecht : 42-54.
Keywords: Gauß's Disquisitiones, binary quadratic forms, quadratic reciprocity law, class number of binary quadratic forms.
Stevenhagen, P. and Lenstra, Hendrik W. Jr. 1996.
Chebotarev and His Density Theorem. Mathematical Intelligencer, vol. 18 no. 2, 26-37
abstracts: Zbl
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Strobl, Walter. 1980?
Desarrollo historico y sistematico de la teoria aritmetica de las funciones algebraicas de Dedekind y Weber. Tesis de licenciatura presentada a la Facultad de matematicas de la Universidad complutense de Madrid. Kaiserlautern, Abteilung Foto-Repro-Druck der Universität Kaiserslautern. 184 p.
Keywords: Dedekind, Weber, function fields, Gauß, Dirichlet, Kummer, Kronecker, Riemann, theorem of Riemann-Roch.
Strobl, Walter. 1981.
Über die Beziehungen zwischen der Dedekindschen Zahlentheorie und der Theorie der algebraischen Funktionen von Dedekind und Weber. Preprint der Universität Kaiserslautern 29.
Keywords: Dedekind, Weber, function fields, Gauß, Dirichlet, Kummer, Kronecker, Riemann, theorem of Riemann-Roch.
Strobl, Walter. 1982.
Über die Beziehungen zwischen der Dedekindschen Zahlentheorie und der Theorie der algebraischen Funktionen von Dedekind und Weber. In Festschrift der Braunschweigischen Wissenschaftlichen Gesellschaft und der Technischen Universität Carolo Wilhelmina zu Braunschweig zur 150. Wiederkehr des Geburtstages von Richard Dedekind. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 33. Göttingen, Goltze: 225-246.
abstracts: Zbl
Keywords: Dedekind, Weber, function fields, Gauß, Dirichlet, Kummer, Kronecker, Riemann, theorem of Riemann-Roch, Riemann surfaces.
Strobl, Walter 1985.
Aus den wissenschaftlichen Anfängen Hermann Minkowskis. Historia Mathematica 12, 142-156.
abstracts: Zbl
Keywords: Minkowski, Weber, quadratic forms, Dedekind, reduction theory of binary quadratic forms, university of Königsberg, Académie des Sciences (Paris).
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Three Aspects of the Theory of Complex Multiplication. In The Intersection of History and Mathematics, edited by Sasaki Chikira, Sugiuru Mitsuo & Joseph Dauben. Science Networks 15. Basel/Boston/Berlin, Birkhäuser: 91-108.
Keywords: complex multiplication
Terjanian, Guy. 1995.
L'œuvre arithmetique de Kummer. Gaz. Math. 66, 45--53.
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On the origins of p-adic analysis. In Symposia Gaußiana. Proceedings of the 2nd Gauß Symposium. Conference - A: Mathematics and Theoretical Physics. Munich, Germany, August 2-7, 1993, edited by Minaketan Behara, Rudolf Fritsch, Rubens G. Lintz. Berlin/New York, de Gruyter: 459-473.
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Ullrich, Peter. 1998.
The genesis of Hensel's p-adic numbers. In Karl der Grossen und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa, edited by P.L Butzer, H. Th. Jongen and W. Oberschelp. Volume 2: Mathematisches Wissen. Turnhout, Brepols: 163-178.
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Die Entdeckung der Analogie zwischen Zahl- und Funktionenkörpern: der Ursprung der ``Dedekind-Ringe''. Jahresbericht der Deutschen Mathematiker-Vereinigung 101: 116-134.
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Ullrich, Peter. 2002
Über das Exemplar der "Disquisitiones arithmeticae" aus dem Besitz von Gotthold Eisenstein. Mitt. Math. Ges. Hamburg 21 (2002), no. 1, 35-58
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Fermat's last theorem seen as an exercise in evolutionary epistemology. In Evolutionary epistemology. A Multiparadigm Program with a Complete Evolutionary Epistemology Bibliography, edited by Werner Callebaut & Pinxten, Rik. Synthese Library, 190. Dordrecht, Reidel: 337-363.
Keywords: Fermat's Last Theorem, philosophy of number theory.
Vladut, S. G. 1983.
On the History of Complex Multiplication. Gauß, Eisenstein, and Kronecker. Istoriko-matematiceskie issledovanija 27: 190-238.
Vladut, S. G. 1991.
Kronecker's Jugendtraum and modular functions. Translated from the Russian by M. Tsfasman. Studies in the Development of Modern Mathematics 2. New York, Gordon and Breach.
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Nineteenth-Century Mathematics in the Mirror of its Literature: A Quantitative Approach. Historia Mathematica 23: 288-318.
abstracts: Zbl
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Waldschmidt, Michel. 1983.
Les débuts de la théorie des nombres transcendants. Cahiers du séminaire d'histoire des mathématiques de l'Institut Henri Poincaré 4: 93-115.
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Waldschmidt, Michel. 1999.
Les débuts de la théorie des nombres transcendants. Serfati, Michel (ed.), La recherche de la vérité Paris, 73-96
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Waterhouse, William. 1984.
A note by Gauß refering to ideals? Historia Mathematica 11: 142-146.
abstracts: Zbl
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Waterhouse, William. 1987.
A neglected note showing Gauß at work. Historia Mathematica 14: 147-156.
abstracts: Zbl
Keywords: Gauß, cyclotomic norms, conjectures.
Weil, André. 1974a.
La cyclotomie jadis et naguère. L'Enseignement mathématique, IIe série 20: 247-263.
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Weil, André. 1974b.
Sommes de Jacobi et caractères de Hecke. Nachrichten der Akademie der Wissenschaften in Göttingen. Mathematisch-physikalische Klasse: 1-14.
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Weil, André. 1974c.
Sur les sommes de trois et quatre carrés. L'Enseignement mathématique, IIe série 20: 215-222.
abstracts: Zbl
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Weil, André. 1974d. Two lectures on number theory, past and present. L'Enseignement mathématique, IIe série 20: 87-110.
abstracts: Zbl
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Weil, André. 1975.
Introduction. In Collected Papers by E. E. Kummer. New York, Springer: 1-11. [=1979. André Weil, Œuvres scientifiques. Collected Papers. Vol. III: 379-389.
Keywords: Kummer.
Weil, André. 1976.
Review of Eisenstein, Gotthold: Mathematische Werke. Bulletin of the American Mathematical Society 82: 658-663.
Keywords: Eisenstein.
Weil, André. 1986.
Gauß et la composition des formes quadratiques, Aspects of Mathematics and its Applications, J. A. Barroso (ed.) North Holland, Amsterdam and New York, 1986: 895-912.
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Weil, André. 1989.
Prehistory of the zeta-function. In Number theory, trace formulas and discrete groups, Symp. in Honor of Atle Selberg, Oslo/Norway 1987, 1-9
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On Eisenstein's copy of the Disquisitiones. In Algebraic Number Theory in honor of K. Iwasawa, edited by John Coates et al. Advanced Studies in Pure Mathematics 17. Tokyo, Academic Press & Kinokuniya: 463-469.
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Weyl, Hermann 1944.
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