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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