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 :
Description

Orateur(s) Rahul Dalal - ,
Titre Root number equidistribution for sef-dual automorphic representations on GL_n
Date02/12/2024
Horaire10:30 à 12:00
Diffusion
Résume

A classical question asks: consider the set of elliptic curves $E/Q$ with conductor less than or equal to $n$. Do the root numbers of the corresponding $L$-functions $L(s,E)$ equidistribute between $\pm 1$ as $n \to \infty$? Assuming the BSD conjecture, this determines which fraction of elliptic curves have even or odd-rank groups of rational points. 

 

We discuss an automorphic-side variant of this question generalized to higher rank. Specifically, consider the set of self-dual cuspidal automorphic representations on GL_n with specific weight at infinity and conductor. We show that for most conductors, the root numbers of the corresponding $L$-functions equidistribute between $\pm 1$ as the weight goes to infinity and exactly classify the conductors for which such equidistribution doesn't hold. We also prove similar results in the conjugate self-dual setting and for the corresponding families of Galois representations whenever they are known to exist. 

Salle15-25 502
AdresseJussieu
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