English
Formulas for the limiting distribution of traces of Frobenius
Post-edited
Auteurs : Lachaud, Gilles (Auteur de la conférence)
CIRM (Editeur )
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
CIRM (Editeur )
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
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 28/04/14 Date de Captation : 11/02/14 Sous Collection : Research School Catégorie arXiv : Algebraic Geometry Domaine(s) : Théorie de LIe ; Théorie des Nombres Format : QuickTime (.mov) Durée : 00:48:58 Audience : Chercheurs Download : https://videos.cirm-math.fr/2014-02-24_Lachaud.mp4 
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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 courbesOrganisateurs de la Rencontre : Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor Dates : 17/02/14 - 28/02/14 Année de la rencontre : 2014 URL de la Rencontre : http://shparlinskikohel.weebly.com/sched...
Données de citation
DOI : 10.24350/CIRM.V.18478403Citer cette vidéo: 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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