Re- and Preprints:

Here's A list of publications.

NEW!

For reprints and updates in pdf format, go to my new page.

Class Groups

  1. The MR-abstract of my paper on Kuroda's Class Number Formula; Acta Arith. 66 (1994), 245--260
  2. On class groups of cyclotomic number fields I; Acta Arith. 72 (1995), 347--359; MR
  3. On class groups of cyclotomic number fields II; Acta Arith. 84 (1998), 59--70
  4. On class groups of cyclotomic number fields III; (coming soon)
  5. On the 4-rank of class groups of real quadratic number fields, with a new proof of C. Maire's result that the 2-class field tower of such fields is infinite if their 4-rank is at least 4.
  6. The solution of the class number 1 problem for CM fields of degree 24 whose Galois group has the alternating group A4 as a quotient (with Stephane Louboutin and Ryotaro Okazaki). Final version. J. Theor. Nombres 11 (1999), 387-406

Reciprocity Laws

  1. On Rational Quartic Reciprocity; Acta Arith. 67 (1994), 387--390; MR
  2. Rational Quartic Reciprocity II ; Acta Arith. 80 (1997), 273--276; generalizes the first part to composite values of the denominator.
  3. Here is a link to my book on the Reciprocity Laws from Euler to Eisenstein. Part II on the development from Kummer to Artin is currently being completed.
  4. An online Bibliography on Reciprocity Laws;
  5. A list of Proofs of the Quadratic Reciprocity Law.

Euclidean Number Fields

  1. A survey on Euclidean Number Fields; also available as a gzipped dvi file. This is an update of the article in Expo. Math. 13 (1995), 385-416. Last update: Oct. 29, 1999. MR
  2. On The Euclidean Algorithm in Cubic Fields (with Stefania Cavallar); Proc. Number Theory Eger 1996 (1998), 123--146;
  3. On Gauss Bounds of quadratic extensions of imaginary quadratic Euclidean number fields; Publ. Math. Debrecen 50 (1997), 365--368
  4. Euclidean Windows (with Stefania Cavallar); LMS J. Comput. Math. 3 (2000), 335-355
  5. A manuscript on the classification of the norm-Euclidean bicyclic complex quartic fields (ps)
  6. An online Bibliography on Euclidean Rings.

Class Field Towers

  1. The MR review of my paper on 2-class field towers of imaginary quadratic number fields; J. Theor. Nombres Bordeaux 6 (1994), 261--272
  2. On the Construction of Hilbert 2-Class Fields is a very short introduction to my thesis;
  3. On unramified quaternion extensions of quadratic number fields; J. Theor. Nombres Bordeaux 9 (1997), 51--68
  4. The determination of all real quadratic number fields whose $2$-class field tower is abelian (with E. Benjamin and C. Snyder); J. Number Theory 73 (1998), 182--194
  5. The determination of all imaginary quadratic number fields whose 2-class field has a cyclic 2-class group (with E. Benjamin and C. Snyder); J. Number Theory 67 (1997), 229--245
  6. On the determination of the 2-class field tower of a certain family of imaginary quadratic number fields; Abh. Math. Sem. Hamburg 67 (1997), 205--214
  7. Imaginary quadratic fields k with Cl_2(k) = (2,2^m) and d(Cl_2(k^1)) = 2 (May 1999, with E. Benjamin and C. Snyder; Pac. J. Math, to appear)
  8. A search for imaginary quadratic number fields with 2-class field tower of length 3 (with E. Benjamin and C. Snyder, in preparation)
  9. A survey on Class Field Towers

Elliptic Curves

  1. They have their own page.
  2. On Tate-Shafarevich groups of some elliptic curves; Algebraic number theory and Diophantine analysis (Graz, 1998), 277--291
  3. A note on Pepin's counter examples to the Hasse Principle for curves of genus 1; Abh. Math. Sem. Hamburg 69 (1999), 335-345. Meanwhile I discovered a beautiful article by Noam Elkies that also mentions the approach to FLT for N = 7 using 2-descent on elliptic curves: be sure to check out "The Klein Quartic in Number Theory" in "The Eightfold Way", S. Levy (Ed.), MSRI Publications 35 (1999), Cambridge Univ. Press.
  4. On the capitulation of Tate-Shafarevich groups (coming soon)
  5. Some families of non-congruent numbers (coming soon)

The Rest

  1. On Simplest Cubic Fields (with A. Pethoe); Manuscripta Math. 88 (1995), 53--58; MR
  2. The Introduction (with Norbert Schappacher) to the English translation of Hilbert's Zahlbericht by I. Adamson that has just been published by Springer Verlag.
  3. A note on the Snake Lemma
  4. On Circles, Primes and Quadratic Residues (draft, June 1999). The final version is in German and called Kreise und Quadrate modulo p, Mathem. Semesterberichte 47 (2000), 51-73
  5. I'm starting to compile a list of Unsolved Problems in algebraic number theory.
  6. Von einer Einfuehrung in die Kohomologie von Gruppen fuer Zahlentheoretiker ist Kapitel I jetzt fertig. An Vorkenntnissen werden algebraische Zahlentheorie (Ideale, p-adische Koerper, Galoistheorie) vorausgesetzt.
  7. Here are some translations of mathematical articles. 
 Last update: Oct 27, 1999