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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Certification of modular Galois representations
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by Nicolas Mascot PDF
Math. Comp. 87 (2018), 381-423 Request permission


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 $26$.
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Additional Information
  • Nicolas Mascot
  • Affiliation: IMB, Université Bordeaux 1, UMR 5251, F-33400 Talence, France – and – CNRS, IMB, UMR 5251, F-33400 Talence, France – and – INRIA, project LFANT, F-33400 Talence, France
  • Address at time of publication: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 1040021
  • Email:
  • Received by editor(s): October 28, 2015
  • Received by editor(s) in revised form: December 9, 2015, and April 6, 2016
  • Published electronically: June 21, 2017
  • Additional Notes: This research was supported by the French ANR-12-BS01-0010-01 through the project PEACE, by the DGA maîtrise de l’information, by ERC Starting Grant ANTICS 278537, and by the EPSRC Programme Grant EP/K034383/1 “LMF: L-Functions and Modular Forms”
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 87 (2018), 381-423
  • MSC (2010): Primary 11Y70, 11S20, 11F80, 11F11, 11Y40, 20B40, 20J06
  • DOI:
  • MathSciNet review: 3716200