SPEAKER: Dorian Goldfeld
TITLE: Multiple Dirichlet series, an historical survey
ABSTRACT:
Multiple Dirichlet series (L-functions of several complex variables) are Dirichlet
series in one complex variable whose coefficients are again Dirichlet series
in other complex variables. These series arise naturally in the theory of
moments of zeta and L-functions. It was found recently by Diaconu-Goldfeld-Hoffstein
that the moment conjectures of random matrix theory, such as the Keating-Snaith
conjecture, would follow if certain multiple Dirichlet series had meromorphic
continuation to a particular tube domain.
We shall present an introduction to some of the basic definitions and techniques
of this theory as well as a survey of some of the results that have been
obtained by this method. These include applications to moments of L-functions,
Fermat's last theorem, classification theory via Dynkin diagrams, and analysis
of natural constructions as inner products of automorphic forms on GL(n).