Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
Name
606925157-MIT.pdf
Description
Full printable version
Size
1.76 MB
Format
Adobe PDF
Checksum (MD5)
84df416f94a0780c72b64ff3aee90f8a
Author(s)
Tabony, Sawyer
Advisor(s)
Benjamin Brubaker.
Date Issued
2009
Publisher
Massachusetts Institute of Technology
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.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 29).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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