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# Post-edited

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Post-edited Formulas for the limiting distribution of traces of Frobenius

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

 Loading the player... 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, See also {14Kxx}
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 Format : QuickTime (.mov) Durée : 00:48:58 Domaine : Lie Theory and Generalizations ; Number Theory Audience : Chercheurs ; Doctorants , Post - Doctorants Download : http://videos.cirm-math.fr/2014-02-24_Lachaud.mp4 Informations sur la rencontre Nom du congrès : Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbesOrganisteurs Congrès : Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, IgorDates : 17/02/14 - 28/02/14 Année de la rencontre : 2014 URL Congrès : http://shparlinskikohel.weebly.com/sched...

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