# Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

 Equipe(s) : fa, tn, Responsables : Alexis Bouthier, Benoît Stroh Email des responsables : alexis.bouthier@imj-prg.fr, benoit.stroh@imj-prg.fr Salle : Adresse : Description

 Orateur(s) Oliver LORSCHEID - Utrecht University, Titre Toroidal automorphic forms for function fields. Date 13/03/2008 Horaire 14:00 à 15:00 Diffusion Résume The definition of a toroidal automorphic form is due to Don Zagier, who showed that the vanishing of certain integrals of Eisenstein series over tori in $GL_2$ is related to the vanishing of the Riemann zeta function at the weight of the Eisenstein series; and thus a relation between the unitarizability of the space of unramified toroidal automorphic forms and the Riemann hypothesis. In this talk, we use an adelic approach for function fields of curves over finite fields. We will prove that in that case, the space of unramified toroidal automorphic forms is finite-dimensional, we will show dimension formulas and we will discuss the connection of unitarizability of toroidal automorphic forms with the Riemann hypothesis for global function fields (which was proven by Andre Weil). Salle Adresse