# Jerusalem Mathematics Colloquium

Thursday, 2nd June 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Wilfried Schmid

(Harvard)

"Automorphic distributions, L-functions and functional equations"

** Abstract: **

Riemann's zeta function encodes deep properties of
prime numbers. Conjecturally Langlands L-functions
do the same for primes in number fields. They are
defined in terms of Euler products. Like the Riemann zeta
function, they should satisfy functional equations. The
functional equations are far from obvious and have been
established only in special cases.

Steve Miller and I have introduced a new method for proving
functional equations. I shall first show how the method
works in the case of the zeta function. I shall then
introduce the notion of an automorphic distribution and
explain how it can be used to prove new results about
L-functions.

Light refreshments will be served in the faculty lounge at 3:30.

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