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Computing congruences of modular forms and Galois representations modulo prime powers
Taixés i Ventosa, Xavier; Wiese, Gabor
2010In Arithmetic, geometry, cryptography and coding theory 2009
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Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Taixés i Ventosa, Xavier
Wiese, Gabor  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Computing congruences of modular forms and Galois representations modulo prime powers
Publication date :
2010
Main work title :
Arithmetic, geometry, cryptography and coding theory 2009
Publisher :
Amer. Math. Soc., Providence, RI, Unknown/unspecified
Collection name :
Contemp. Math.
Pages :
145--166
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 20 November 2013

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