Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes

Collection Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes

Organizer(s) Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor

Date(s) 17/02/2014 - 28/02/2014

linked URL http://shparlinskikohel.weebly.com/schedule-week-2.html

00:00:00 / 00:00:00

18 19

Chapters

Formulas for the limiting distribution of traces of Frobenius

By Gilles Lachaud

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.

Information about the video

Date of recording 11/02/2014
Date of publication 28/04/2014
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18478403
Cite this video Lachaud, Gilles (11/02/2014). Formulas for the limiting distribution of traces of Frobenius. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18478403
URL https://dx.doi.org/10.24350/CIRM.V.18478403

Domain(s)

Algebraic Geometry

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

All the collection videos

56:28

published on October 9, 2014

Distributions of Frobenius of elliptic curves #1

By Chantal David

58:51

published on October 9, 2014

The generalized Sato-Tate conjecture

By Francesc Fité

01:02:28

published on October 9, 2014

The Chebotarev density theorem

By Peter Stevenhagen

01:03:37

published on October 9, 2014

Introduction to Sato-Tate distributions

By Andrew Sutherland

01:00:46

published on October 9, 2014

Distributions of Frobenius of elliptic curves #2

By Chantal David

53:52

published on October 9, 2014

Sato-Tate axioms

By Francesc Fité

58:24

published on May 12, 2014

Distributions of Frobenius of elliptic curves #3

By Nathan Jones

59:05

published on October 9, 2014

Group structures of elliptic curves #1

By Igor Shparlinski

01:04:04

published on October 9, 2014

The Galois type of an Abelian surface

By Francesc Fité

59:43

published on October 9, 2014

Group structures of elliptic curves #2

By Igor Shparlinski

01:05:45

published on October 9, 2014

Character sums for primitive root densities

By Peter Stevenhagen

58:05

published on October 9, 2014

Moment sequences of Sato-Tate groups

By Andrew Sutherland

01:02:04

published on October 9, 2014

Distributions of Frobenius of elliptic curves #5

By Chantal David

01:04:12

published on October 9, 2014

Distributions of Frobenius of elliptic curves #4

By Nathan Jones

45:15

published on October 9, 2014

Distributions of Frobenius of elliptic curves #6

By Nathan Jones

59:40

published on October 9, 2014

Group structures of elliptic curves #3

By Igor Shparlinski

01:11:18

published on October 9, 2014

Computing Sato-Tate statistics

By Andrew Sutherland

48:58

published on April 28, 2014

Formulas for the limiting distribution of traces of Frobenius

By Gilles Lachaud

01:00:03

published on October 20, 2014

Distributions des valeurs propres des Frobenius des variétés abéliennes sur un corps fini donné

By Jean-Pierre Serre

Copyright Carmin.tv 2024

Give feedback