Bretton Woods Schedule

MONDAY, July 11, 2005.
Afternoon:

• 2-2:15 Introduction
• 2:15-3:45 Sol Friedberg (Multiple Dirichlet Series and Automorphic Forms: I)
• 3:45-4:15 coffee/tea break
• 4:15-5:15 Gautam Chinta (Multiple Dirichlet Series and Automorphic Forms: II)

TUESDAY, July 12, 2005.
Morning:

• 9:00-10:30 Dan Bump (Weyl Group Multiple Dirichlet Series: I)
• 10:30-11:00 coffee/tea break
• 11-12:30 Ben Brubaker (Weyl Group Multiple Dirichlet Series: II)

• 2:00-3:00 Ram Murty (Dirichlet series and hyperelliptic curves)
• 3:00-3:30 coffee/tea break
• 3:30-4:30 Matti Jutila (Uniform bounds for Rankin-Selberg L-functions)

WEDNESDAY, July 13, 2005
Morning:

• 9:00-10:00 Gautam Chinta (Multiple Dirichlet Series and Automorphic Forms: III)
• 10:00-10:15 coffee/tea break
• 10:15-11:15 Adrian Diaconu, (Integral moments of automorphic L-functions over imaginary quadratic fields)
• 11:30-12:30 Anton Deitmar (Generalized Selberg Zeta Functions)

THURSDAY, July 14, 2005
Morning:

• 9:00-10:00 Ken Ono ((Traces of singular moduli and Maass-Poincare series)
• 10:00-10:15 coffee/tea break
• 10:15-11:15 Qaio Zhang (integral mean values of Maass L-functions)
• 11:30-12:15 Ozlem Imamoglu, (representations of integers as sums of an even number of squares)

• 2:00-2:45 Jyoti Sengupta (Sign changes of Hecke eigenvalues of cusp forms)
• 2:50-3:35 P.M. Martin Huxley (Is the Hlawka zeta function a valid object?)
• 3:40-4:25 P.M. Wladimir Pribitkin (Double sums of Kloosterman Sums)
• 4:30-5:15 P.M. Joe Hundley: Some new Rankin-Selberg Integrals on Orthogonal Groups

Syllabi for Mini-Courses

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.