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Certification of modular Galois representations


Author: Nicolas Mascot
Journal: Math. Comp.
MSC (2010): Primary 11Y70, 11S20, 11F80, 11F11, 11Y40, 20B40, 20J06
DOI: https://doi.org/10.1090/mcom/3215
Published electronically: June 21, 2017
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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$.


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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
Email: n.a.v.mascot@warwick.ac.uk

DOI: https://doi.org/10.1090/mcom/3215
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”
Article copyright: © Copyright 2017 American Mathematical Society