Estimées pour les valuations $p$-adiques des valeurs propres des opérateurs de Hecke

Abstract

For cuspidal automorphic forms on function fields and for cohomological cuspidal automorphic forms on number fields we give estimates for the p-adic valuations of eigenvalues of Hecke operators. In the case of number fields, these estimates correspond to Katz-Mazur estimates by the Langlands conjectures.