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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula

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dc.contributor.advisor Benjamin Brubaker. en_US Tabony, Sawyer en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2010-04-28T17:17:08Z 2010-04-28T17:17:08Z 2009 en_US 2009 en_US
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 29). en_US
dc.description.abstract 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. en_US
dc.description.statementofresponsibility by Sawyer Tabony. en_US
dc.format.extent 29 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula en_US
dc.type Thesis en_US S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 606925157 en_US

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