Multiple Dirichlet Series L functions and Automorphic Forms 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). 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.