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Mascot, Nicolas (2017) Certification of modular Galois representations. Mathematics of Computation, 87 . pp. 381-423. doi:10.1090/mcom/3215 ISSN 0025-5718.
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Official URL: https://doi.org/10.1090/mcom/3215
Abstract
We show how the output of the algorithm to compute modular Galois representations previously described by the author [Rend. Circ. Mat. Palermo (2) 62 (2013), no. 3, 451-476] can be certified. We have used this process to compute certified tables of such Galois representations obtained thanks to an improved version of this algorithm, including representations modulo primes up to $ 31$ and representations attached to a newform with nonrational (but of course algebraic) coefficients, which had never been done before. These computations take place in the Jacobian of modular curves of genus up to $ 26$.
| 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): | Galois theory , Forms, Modular | |||||||||
| Journal or Publication Title: | Mathematics of Computation | |||||||||
| Publisher: | American Mathematical Society | |||||||||
| ISSN: | 0025-5718 | |||||||||
| Official Date: | 21 June 2017 | |||||||||
| Dates: |
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| Volume: | 87 | |||||||||
| Page Range: | pp. 381-423 | |||||||||
| DOI: | 10.1090/mcom/3215 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | “First published in Mathematics of Computation in 87.2017, published by the American Mathematical Society,” and the copyright notice in proper form must be placed on all copies. | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Copyright Holders: | © Copyright 2017 American Mathematical Society | |||||||||
| Date of first compliant deposit: | 20 September 2019 | |||||||||
| Date of first compliant Open Access: | 20 September 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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