Graduate Number Theory Seminar
Dylon Chow
UIC
An introduction to Tate's Thesis
Abstract: In this talk I will discuss Tate's 1950 Ph.D. thesis, which gives the theory of automorphic representations and L-functions of GL(1). Tate used harmonic analysis on adele groups to reprove Hecke's theorems on the functional equations of L-functions attached to Hecke characters. This approach provides greater conceptual simplification and clarity than can be found in the classical techniques used by Hecke. In fact, Tate showed that the results of Hecke are more or less an application of a general form of the Poisson summation formula. In this talk I will define the adeles and ideles, discuss the adelic Poisson summation formula, and outline an adelic proof of the meromorphic continuation and functional equation of the Riemann zeta function.
Monday November 4, 2013 at 3:00 PM in SEO 427