Wednesday, November 9
Milner 317, 12:30 PM
Title: Eisenstein series, L-functions, and Young tableaux
Abstract: The Fourier coefficients of Eisenstein series contain interesting arithmetic objects. As a protoexample, Maass introduced an Eisenstein series on GL(2) whose constant coefficient contained the Riemann zeta function, so analytic continuation of the Eisenstein series implies another proof of the analytic continuation of the zeta function. In this talk, we'll discuss Eisenstein series on certain covers of classical Lie groups, why you'd never want to compute their Fourier coefficients using an integral with an additive character, and how you can get around it using combinatorics involving Young tableaux. These Eisenstein series on covers have Fourier coefficients that can contain Dirichlet L-series, L-functions of higher rank automorphic forms, and other interesting functions to be discussed, from which we derive arithmetic applications.