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P-adic L-functions for GL(2)
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Barrera Salazar, Daniel and Williams, Christopher David (2019) P-adic L-functions for GL(2). Canadian Journal of Mathematics, 71 (5). pp. 1019-1059. doi:10.4153/CJM-2017-062-0 ISSN 0008-414X.
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Official URL: https://doi.org/10.4153/CJM-2017-062-0
Abstract
Since Rob Pollack and Glenn Stevens used overconvergent modular symbols to construct -adic -functions for non-critical slope rational modular forms, the theory has been extended to construct -adic -functions for non-critical slope automorphic forms over totally real and imaginary quadratic fields by the first and second authors, respectively. In this paper, we give an analogous construction over a general number field. In particular, we start by proving a control theorem stating that the specialisation map from overconvergent to classical modular symbols is an isomorphism on the small slope subspace. We then show that if one takes the modular symbol attached to a small slope cuspidal eigenform, then one can construct a ray class distribution from the corresponding overconvergent symbol, which moreover interpolates critical values of the -function of the eigenform. We prove that this distribution is independent of the choices made in its construction. We define the -adic -function of the eigenform to be this distribution.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Algebraic number theory, L-functions | ||||||||||||
| Journal or Publication Title: | Canadian Journal of Mathematics | ||||||||||||
| Publisher: | Cambridge University Press | ||||||||||||
| ISSN: | 0008-414X | ||||||||||||
| Official Date: | October 2019 | ||||||||||||
| Dates: |
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| Volume: | 71 | ||||||||||||
| Number: | 5 | ||||||||||||
| Page Range: | pp. 1019-1059 | ||||||||||||
| DOI: | 10.4153/CJM-2017-062-0 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Canadian Journal of Mathematics. https://doi.org/10.4153/CJM-2017-062-0 This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Canadian Mathematical Society 2018 | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | © Canadian Mathematical Society 2018 | ||||||||||||
| Date of first compliant deposit: | 18 October 2019 | ||||||||||||
| Date of first compliant Open Access: | 18 October 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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