Single angle On equality of arithmetic and analytic exterior square root numbers
Auteurs : Shahidi, Freydoon (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : This is a joint work with J. Cogdell and T.-L. Tsai. I will report on the progress made in proving the equality of Artin epsilon factors for exterior and symmetric square L-functions with those on the representation theoretic side through the local Langlands correspondence. The equality for L-functions has already been established by Henniart. I will show how the equality can be proved if one has the stability of these factors under highly ramified twists for supercuspidal representations. I will then discuss the stability question for supercuspidals by discussing how it can be deduced from a generalization of germ expansions of Jacquet and Ye from Bessel functions to certain partial Bessel functions. I will elaborate by explaining the stability in the case of GL(2) through general lemmas proved so far.11F66 - Langlands L-functions; one variable Dirichlet series and functional equations
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
11F80 - Galois representations
22E50 - Representations of Lie and linear algebraic groups over local fields