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Mathematics > Number Theory

arXiv:0909.2724 (math)
[Submitted on 15 Sep 2009 (v1), last revised 21 Jan 2010 (this version, v2)]

Title:Computing Congruences of Modular Forms and Galois Representations Modulo Prime Powers

Authors:Xavier Taixes i Ventosa, Gabor Wiese
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Abstract: This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials have a root in common in a sense that is defined. These techniques are applied to the study of congruences of modular forms and modular Galois representations modulo prime powers. Finally, some computational results with implications on the (non-)liftability of modular forms modulo prime powers and possible generalisations of level raising are presented.
Comments: 26 pages
Subjects: Number Theory (math.NT)
MSC classes: 11F33 (primary); 11F11, 11F80, 11Y40.
Cite as: arXiv:0909.2724 [math.NT]
  (or arXiv:0909.2724v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.0909.2724

Submission history

From: Gabor Wiese [view email]
[v1] Tue, 15 Sep 2009 07:02:34 UTC (25 KB)
[v2] Thu, 21 Jan 2010 17:24:17 UTC (27 KB)
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