Central to the modern analytic theory of automorphic forms (such as the classical holomorphic modular forms) is the notion of a family. Several definitions of a family have been proposed, all of which involve a finite set of cusp forms on a reductive linear group (such as GL(2)), described by a natural condition and expanding in size. The cardinality of the expanding set acts as an essential characteristic of a family; for example, in the case of the “universal family”, it is related to the number of requisite twists in the Converse Theorem as well as to the Sobolev norms studied by Michel-Venkatesh. In this talk, I will present new asymptotic results on counting automorphic forms in the universal families and Hecke characters as well as associated results on explicit uniform Weyl laws and limit multiplicity theorems. This will be a survey talk, with emphasis on the underlying intuition. This work is joint with Farrell Brumley.
Mittwoch, den 15. Juni 2016 um 11 Uhr c.t. Uhr, in Mathematikon, INF 205, Seminarraum 4, 3. OG Mittwoch, den 15. Juni 2016 at 11 Uhr c.t., in Mathematikon, INF 205, Seminarraum 4, 3. OG
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Kohnen