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P-adic L-functions of Bianchi modular forms
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Williams, Christopher David (2017) P-adic L-functions of Bianchi modular forms. Proceedings of the London Mathematical Society, 114 (4). pp. 614-656. doi:10.1112/plms.12020 ISSN 0024-6115.
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Official URL: https://doi.org/10.1112/plms.12020
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 paper, we give an analogue of their results for Bianchi modular forms, that is, modular forms over imaginary quadratic fields. In particular, we prove control theorems that say that the canonical specialisation map from overconvergent to classical Bianchi modular symbols is an isomorphism on small slope eigenspaces of suitable Hecke operators. We also give an explicit link between the classical modular symbol attached to a Bianchi modular form and critical values of its L ‐function, which then allows us to construct p ‐adic L ‐functions of Bianchi modular forms.
| 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): | P-adic numbers, L-functions, Forms, Modular, Algebraic number theory | ||||||||
| Journal or Publication Title: | Proceedings of the London Mathematical Society | ||||||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||
| ISSN: | 0024-6115 | ||||||||
| Official Date: | April 2017 | ||||||||
| Dates: |
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| Volume: | 114 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 614-656 | ||||||||
| DOI: | 10.1112/plms.12020 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 17 October 2019 | ||||||||
| Date of first compliant Open Access: | 17 October 2019 |
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