Séminaire d'arithmétique à Lyon

Equidistribution of exponential sums over finite fields

by Arthur Forey (EPFL)

Europe/Paris
M7.411 (ENS Lyon, UMPA)

M7.411

ENS Lyon, UMPA

Description

Many exponential sums over finite fields, such as Gauss or Salié-Kloosterman sums, appear as the Fourier-Melin transform of the trace function of an l-adic sheaf on a commutative algebraic group. We are interested in the equidistribution of such sums as the character varies. Generalizing work by Deligne and Katz in the cases of additive and multiplicative groups, a Tannakian formalism always controls the equidistribution. This is a collaboration with Javier Fresán and Emmanuel Kowalski.