Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Francesco Lemma
Email des responsables : alexis.bouthier@imj-prg.fr, francesco.lemma(at)imj-prg.fr
Salle :
Adresse :

Orateur(s) Jeanine van ORDER - EPFL Lausanne,
Titre Generic nonvanishing of $GL_2$ Rankin-Selberg L-values (and beyond).
Horaire10:30 à 11:30
RésumeWe consider Rankin-Selberg L-functions of $GL_2$ over totally real number fields, in particular corresponding to Hilbert modular eigenforms of parallel weights two and one. Here, the weight two form f is cuspidal (and fixed), and the weight one form $g_W$ is the theta series associated to some Hecke character W of a CM extension of the totally real base field (which we vary). Such L-functions are not necessarily self-dual, and the well known special value formulae of Waldspurger, Gross-Zagier et alia do not typically apply. In the general setting where the (central) critical values are not forced to vanish by the functional equation, I will explain how a combination of analytic averaging techniques with the existence of some associated p-adic L-function can be used to deduce positive density nonvanishing properties for families of special values, thus extending the relevant theorems of Rohrlich, Vatsal and Cornut-Vatsal. If time permits, then I will also explain some open problems that can likely be addressed via similar techniques.