En utilisant le lien entre représentations galoisiennes et formes modulaires provenant de la Conjecture de Serre, nous calculons, pour tout premier , une borne pour le nombre de classes d’isomorphismes des représentations galoisiennes de sur un –espace vectoriel de dimension deux qui sont irréductibles, impaires, et non–ramifiées en dehors de .
Using the link between Galois representations and modular forms established by Serre’s Conjecture, we compute, for every prime , a lower bound for the number of isomorphism classes of Galois representation of on a two–dimensional vector space over which are irreducible, odd, and unramified outside .
@article{JTNB_2011__23_3_603_0,
author = {Tommaso Giorgio Centeleghe},
title = {Computing the number of certain {Galois} representations mod $p$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {603--627},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {23},
number = {3},
year = {2011},
doi = {10.5802/jtnb.779},
mrnumber = {2861077},
zbl = {1261.11044},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.779/}
}
TY - JOUR AU - Tommaso Giorgio Centeleghe TI - Computing the number of certain Galois representations mod $p$ JO - Journal de théorie des nombres de Bordeaux PY - 2011 SP - 603 EP - 627 VL - 23 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.779/ DO - 10.5802/jtnb.779 LA - en ID - JTNB_2011__23_3_603_0 ER -
%0 Journal Article %A Tommaso Giorgio Centeleghe %T Computing the number of certain Galois representations mod $p$ %J Journal de théorie des nombres de Bordeaux %D 2011 %P 603-627 %V 23 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.779/ %R 10.5802/jtnb.779 %G en %F JTNB_2011__23_3_603_0
Tommaso Giorgio Centeleghe. Computing the number of certain Galois representations mod $p$. Journal de théorie des nombres de Bordeaux, Tome 23 (2011) no. 3, pp. 603-627. doi : 10.5802/jtnb.779. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.779/
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