Français
Formulas for the limiting distribution of traces of Frobenius
Post-edited
Authors : Lachaud, Gilles (Author of the conference)
CIRM (Publisher )
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 (Publisher )
Abstract :
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.
MSC Codes : 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
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/04/14 Conference Date : 11/02/14 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Lie Theory and Generalizations ; Number Theory Format : QuickTime (.mov) Video Time : 00:48:58 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2014-02-24_Lachaud.mp4 
|
Information on the Event
Event Title : Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbesEvent Organizers : Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor Dates : 17/02/14 - 28/02/14 Event Year : 2014 Event URL : http://shparlinskikohel.weebly.com/sched...
Citation Data
DOI : 10.24350/CIRM.V.18478403Cite 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 |
Bibliography
