Computing the number of certain Galois representations mod p
Journal de Théorie des Nombres de Bordeaux, Tome 23 (2011) no. 3, pp. 603-627.

En utilisant le lien entre représentations galoisiennes et formes modulaires provenant de la Conjecture de Serre, nous calculons, pour tout premier p2593, une borne pour le nombre de classes d’isomorphismes des représentations galoisiennes de Q sur un F ¯ p –espace vectoriel de dimension deux qui sont irréductibles, impaires, et non–ramifiées en dehors de p.

Using the link between Galois representations and modular forms established by Serre’s Conjecture, we compute, for every prime p2593, a lower bound for the number of isomorphism classes of Galois representation of Q on a two–dimensional vector space over F ¯ p which are irreducible, odd, and unramified outside p.

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DOI : https://doi.org/10.5802/jtnb.779
@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},
     zbl = {1261.11044},
     mrnumber = {2861077},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.779/}
}
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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