Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula

• Main Author: Tabony, Sawyer
• Other Authors: Benjamin Brubaker.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2010
• Subjects: Mathematics.
• Online Access: http://hdl.handle.net/1721.1/54665

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. === Cataloged from PDF version of thesis. === Includes bibliographical references (p. 29). === In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series defined using Gauss sums, in order to demonstrate the arithmetic content. In this paper we reexamine this connection in the particular case that was discussed in Metaplectic Forms. By looking through the scope of twisted multiplicativity, a property of L-series, the computation is simplified and more easily generalized. === by Sawyer Tabony. === S.M.