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H 1 Formulas for the limiting distribution of traces of Frobenius

Auteurs : Lachaud, Gilles (Auteur de la Conférence)
CIRM (Editeur )

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symplectic group integration formula of Weyl equidistribution of traces Katz-Sarnak theory Sato-Tate conjecture distribution of the trace curves of genus 2 Legendre function Meijer G-function Legendre elliptic integrals Viète's way Viète map Girard's formula the second trace formula for g=3
Résumé : We discuss the distribution of the trace of a random matrix in the compact Lie group USp2g, with the normalized Haar measure. According to the generalized Sato-Tate conjecture, if A is an abelian variety of dimension g defined over the rationals, the sequence of traces of Frobenius in the successive reductions of A modulo primes appears to be equidistributed with respect to this distribution. If g = 2, we provide expressions for the characteristic function, the density, and the repartition function of this distribution in terms of higher transcendental functions, namely Legendre and Meijer functions.

Codes MSC :
11G05 - Elliptic curves over global fields
 11G10 - Abelian varieties of dimension >1
 14G10 - Zeta-functions and related questions
 37C30 - Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 28/04/14
    Date de captation : 11/02/14
    Collection : Research talks ; Lie Theory and Generalizations ; Number Theory
    Format : QuickTime (.mov) Durée : 00:48:58
    Domaine : Lie Theory and Generalizations ; Number Theory
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2014-02-24_Lachaud.mp4
Informations sur la rencontre

Nom de la rencontre : Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes
Organisateurs de la rencontre : Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor
Dates : 17/02/14 - 28/02/14
Année de la rencontre : 2014
URL Congrès : http://shparlinskikohel.weebly.com/sched...

Citation Data

DOI : 10.24350/CIRM.V.18478403
Cite this video as: Lachaud, Gilles (2014). Formulas for the limiting distribution of traces of Frobenius. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18478403
URI : http://dx.doi.org/10.24350/CIRM.V.18478403

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