P r e f a c e
This volume represents the proceedings of the Bretton Woods Workshop on
Multiple Dirichlet Series which took place at the Mount Washington Hotel in Bret-
ton Woods, New Hampshire during the period July 11-14, 2005. The workshop
was organized by Daniel Bump, Solomon Friedberg, Dorian Goldfeld, and Jeffrey
Hoffstein, and was funded by an NSF Focussed Research Group grant1.
Multiple Dirichlet series are Dirichlet series in several complex variables. A
multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional
equations and has meromorphic continuation everywhere. The earliest examples
came from Mellin transforms of metaplectic Eisenstein series and were intensively
studied over the last twenty years by the organizers above and their students.
More recently, many other examples have been discovered and it appears that
all the classical theorems on moments of L-functions as well as the conjectures
(such as those predicted by random matrix theory) can now be obtained via the
theory of multiple Dirichlet series. Furthermore, new results, not obtainable by
other methods, are just coming to light. It was felt that the subject had sufficiently
developed that an account of some of the major results to date and the opportunities
for the future should be recorded at this time. The pristine environment of the
White Mountains and the hospitality of the Mount Washington Hotel provided an
ideal venue to bring together researchers from around the world working in multiple
Dirichlet series and allied fields.
The workshop was centered around the following four themes:
• An exposition of the main results in the theory of multiple Dirichlet series,
• Moments of zeta and L-functions,
• New examples of multiple Dirichlet series,
• Connections with allied fields.
These themes appear in the papers of this volume in different mixes. The contri-
butions of Brubaker-Bump, Brubaker-Bump-Chinta-Friedberg-Hoffstein, Chinta-
Friedberg-Hoffstein, Deitmar, Diaconu-Goldfeld, Masri, Murty-Sinha, and Zhang
offer overviews of or new developments concerning multiple Dirichlet series. These
papers are presented in the first part of this volume, which is arranged thematically,
so that one can obtain an overview of the field by reading the papers consecutively.
Almost all of these papers describe connections to related fields as well. The papers
of Choie-Diamantis, Ginzburg, Huxley, Ivic, Jutila-Motohashi, Motohashi, Moz-
zochi, and Rudnick-Soundararajan concern the allied fields of automorphic forms
grants DMS-0354662 (Bump), DMS-0353964 (Friedberg), DMS-0354582 (Goldfeld),
and DMS-0354534 (Hoffstein).