Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

 Equipe(s) : fa, tn, Responsables : Alexis Bouthier, Cong Xue Email des responsables : alexis.bouthier@imj-prg.fr, cong.xue@imj-prg.fr Salle : Adresse : Description

 Orateur(s) Jeanine Van Order - Max Planck Institute for Mathematics, Titre Dirichlet twisting of $\operatorname{GL}(n)$-automorphic L-functions Date 16/03/2015 Horaire 10:00 à 12:30 Diffusion Résume Let $\pi$ be a cuspidal automorphic representation of $\mathrmGL(n)$ over a number field $F$, whose Satake parameters are algebraic numbers. Fix a rational prime $p$, and let $X$ be the set of all finite-order idele class characters of $F$ obtained by composition with the norm homomorphism from $F$ to $\mathbb Q$ with some Dirichlet character of $p$-power conductor. I will explain why one should expect that for all but finitely many characters $\xi$ in the set $X$, the central value $L(1/2, \pi \times \xi)$ does not vanish, as well as some results in special cases. Salle Adresse