Multiple Dirichlet Series, L-functions and Automorphic Forms

✍ Scribed by Daniel Bump (auth.), Daniel Bump, Solomon Friedberg, Dorian Goldfeld (eds.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 367
• Series: Progress in Mathematics 300
• Edition: 1
• Category: Library

✦ Synopsis

Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions.

Contributors:
J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

✦ Table of Contents

Front Matter....Pages i-viii
Introduction: Multiple Dirichlet Series....Pages 1-36
A Crystal Definition for Symplectic Multiple Dirichlet Series....Pages 37-63
Metaplectic Ice....Pages 65-92
Metaplectic Whittaker Functions and Crystals of Type B....Pages 93-118
Littelmann Patterns and Weyl Group Multiple Dirichlet Series of Type D ....Pages 119-130
Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series....Pages 131-146
Natural Boundaries and Integral Moments of L-Functions....Pages 147-172
A Trace Formula of Special Values of Automorphic L-Functions....Pages 173-191
The Adjoint L -Function of SU 2, 1 ....Pages 193-204
Symplectic Ice....Pages 205-222
On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III....Pages 223-286
A Pseudo Twin Primes Theorem....Pages 287-298
Principal Series Representations of Metaplectic Groups Over Local Fields....Pages 299-327
Excerpt from an Unwritten Letter....Pages 329-338
Two-Dimensional Adelic Analysis and Cuspidal Automorphic Representations of GL(2)....Pages 339-361

✦ Subjects

Number Theory;Group Theory and Generalizations;Mathematical Physics;Combinatorics;Special Functions;Quantum Field Theories, String Theory