Milner 317

Wednesdays, 12:30-1:30 PM

Stanford University

**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.