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 :

Orateur(s) Jeanine Van Order - Max Planck Institute for Mathematics,
Titre Dirichlet twisting of $\operatorname{GL}(n)$-automorphic L-functions
Horaire10:00 à 12:30
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.