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) Anantharam RAGHURAM - Oklahoma State University,
Titre Special values of some automorphic $L$-functions
Horaire14:00 à 15:00
RésumeIn the first half of my talk I will begin with a classical theorem of Shimura on the critical values of the $L$-function of a holomorphic modular form. With this in the background I will then talk about Deligne's conjecture on the critical values of motivic $L$-functions while emphasizing the statement of this conjecture for symmetric power $L$-functions. In the second half of my talk I will describe some recent results of mine, partly in collaboration with Freydoon Shahidi, on the special values of Rankin-Selberg $L$-functions for $GL(n)\times GL(n-1)$. I will explain how we can use recent progress on Langlands functoriality to get results for the critical values of (odd) symmetric power $L$-functions. Time permitting, I hope to end my talk by sketching some work in progress, jointly with Günter Harder, on ratios of critical values.