{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/54665"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/54665","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Tabony, Sawyer"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula"]}]}],"canonical_facts":{"dc:contributor.advisor":["Benjamin Brubaker."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. 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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."],"dc:description.degree":["S.M."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/54665"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"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."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:33Z"}