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. Mc Namara, S.J. Patterson, M. Suzuki, H. Tsumura.
Table des matières
Preface.- Introduction: Multiple Dirichlet Series.- A Crystal Description for Symplectic Multiple Dirichlet Series.- Metaplectic Whittaker Functions and Crystals of Type B.- Metaplectic Ice.- Littelmann patterns and Weyl Group Multiple Dirichlet Series of Type D.- Toroidal Automorphic Forms, Waldspurger Periods and Double Dirichlet Series.- Natural Boundaries and Integral Moments of L-functions.- A Trace Formula of Special Values of Automorphic L-functions.- The Adjoint L-function of SU(2, 1).- Symplectic Ice.- On Witten Multiple Zeta-Functions Associated with Semisimple Lie Algebras III.- A Pseudo Twin-Prime Theorem.- Principal Series Representations of Metaplectic Groups over Local Fields.- Two-Dimensional Adelic Analysis and Cuspidal Automorphic Representations of GL(2).
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