MONDAY, July 11, 2005.
TUESDAY, July 12, 2005.
WEDNESDAY, July 13, 2005
THURSDAY, July 14, 2005
1. Multiple Dirichlet series and automorphic forms
Speakers: Solomon Friedberg, Gautam Chinta
In this series, the speakers will discuss multiple Dirichlet series arising from sums of twisted automorphic L-functions. The series will begin with an historical overview, explaining how such series arise from Rankin-Selberg constructions. Then more recent work, using Hartog's continuation principle in place of such constructions, will be described. Applications to the nonvanishing of L-functions and to other problems will also be discussed.
2. Weyl Group Multiple Dirichlet Series
Speakers: Daniel Bump, Ben Brubaker
In this series, the speakers will explain how to attach a multiple Dirichlet series to each reduced root system and each sufficiently large integer n. The Dirichlet series are functions of r variables, where r is the rank of the root system. They contain arithmetic information of fundamental importance. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each nonzero coefficient is a product of n-th order Gauss sums. The root system plays a basic role in the combinatorics underlying the proof of the functional equations. They will also illustrate the principle that the residues of these roots systems are connected to other interesting multiple Dirichlet series.