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H 0 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

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 13/10/14
      Date de captation : 28/01/14
      Collection : Research talks ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 01:07:05
      Domaine : Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-01-28_Shahidi.mp4

    Informations sur la rencontre

    Nom de la rencontre : Representations of p-adic reductive groups and applications / Représentations des groupes réductifs p-adiques et applications
    Organisateurs de la rencontre : Minguez, Alberto ; Secherre, Vincent ; Shaun, Stevens
    Dates : 27/01/14 - 31/01/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18607403
    Cite this video as: Shahidi, Freydoon (2014). On equality of arithmetic and analytic exterior square root numbers.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.18607403
    URI : http://dx.doi.org/10.24350/CIRM.V.18607403