Reference : Computing congruences of modular forms and Galois representations modulo prime powers
Parts of books : Contribution to collective works
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/11533
Computing congruences of modular forms and Galois representations modulo prime powers
English
Taixés i Ventosa, Xavier [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2010
Arithmetic, geometry, cryptography and coding theory 2009
Amer. Math. Soc.
Contemp. Math.
145--166
Yes
Providence, RI
[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.
http://hdl.handle.net/10993/11533
10.1090/conm/521/10279
http://dx.doi.org/10.1090/conm/521/10279

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