Computing congruences of modular forms and Galois representations modulo prime powers

Reference : Computing congruences of modular forms and Galois representations modulo prime powers


	Document type :	Parts of books : Contribution to collective works
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/11533

Title :	Computing congruences of modular forms and Galois representations modulo prime powers
Language :	English
Author, co-author :	Taixés i Ventosa, Xavier [> >]
	Wiese, Gabor [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2010
Main document title :	Arithmetic, geometry, cryptography and coding theory 2009
Publisher :	Amer. Math. Soc.
Collection and collection volume :	Contemp. Math.
Pages :	145--166
Peer reviewed :	Yes
City :	Providence, RI
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.
Permalink :	http://hdl.handle.net/10993/11533
DOI :	10.1090/conm/521/10279
Other URL :	http://dx.doi.org/10.1090/conm/521/10279

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