In the last 40 years it has been understood that there is a close connection between the spectral theory of hyperbolic manifolds and the theory of L-functions attached to automorphic forms. Trace formulas of Selberg and Kuznetsov-Bruggeman are extremely useful in studying the spectrum and eigenfunctions of the hyperbolic Laplacian. Surprising connections have also been discovered between subconvexity estimates for L-functions and the equidistribution results for Eisenstein series and cusp forms.
Analytical questions about families of L-functions include questions about the distributions of zeros and GRH, value-distribution, special values and applications, as well as connections with arithmetical questions (such as distribution of primes, size of class groups, analytic ranks of elliptic curves). One of the most fruitful approaches to the study of statistical properties of zeros of L-functions involves establishing connections with random matrix theory.
The goal of this workshop is to bring together leading researchers in those fields, to introduce young researchers and graduate students to the state of the art results and to give an account of applications of techniques from analytic number theory to problems in analysis.
The workshop will coincide with the second series of Aisenstadt lectures for the year, to be given by Professor Peter Sarnak.
We wish to acknowledge The National Science Foundation (NSF) for their contribution
(NSF grant DMS-0339017).