The -adic gamma function and the congruences of Atkin and Swinnerton-Dyer
The Local Converse Problem is to determine how the family of the local gamma factors characterizes the isomorphism class of an irreducible admissible generic representation of , with a non-archimedean local field, where runs through all irreducible supercuspidal representations of and runs through positive integers. The Jacquet conjecture asserts that it is enough to take . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...
Nous montrons dans le cas simple du groupe linéaire général, comment on peut déduire de [V. Heiermann 2004] des informations précises sur le degré formel d’une représentation de carré intégrable d’un groupe -adique.