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Overconvergent modular symbols over number fields
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Williams, Christopher David (2016) Overconvergent modular symbols over number fields. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3062990~S1
Abstract
The theory of overconvergent modular symbols, developed by Rob Pollack and Glenn Stevens, gives a beautiful and effective construction of the p-adic L-function of a modular form. In this thesis, we develop the theory of overconvergent modular symbols over a completely general number field and use it to construct p-adic L-functions for automorphic forms for GL2. In particular, we prove control theorems that say that the natural specialisation map from overconvergent to classical modular symbols is an isomorphism on the small slope subspaces, hence attaching a unique overconvergent modular symbol to a small slope cuspidal automorphic eigenform .Φ. From this overconvergent symbol we then obtain a p-adic distribution that interpolates certain critical L-values of .Φ.
The text is comprised of two largely independent parts. In the first, we develop the theory in concrete detail over imaginary quadratic fields, and in the process present a constructive definition of the p-adic L-function in this setting. In the second, which was joint work with Daniel Barrera Salazar (Université de Montréal), we provide an analogous theory over general number fields, though not in the same explicit detail.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Mathematics, Algebraic number theory, L-functions, p-adic numbers, Forms, Modular | ||||
Official Date: | June 2016 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Loeffler, David | ||||
Sponsors: | Centre de recherche en mathématiques de Bordeaux, Iovita, Adrian | ||||
Extent: | xviii, 190 leaves | ||||
Language: | eng |
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