Quadratic Twists of Central Values For GL(3)

Kuan, Chan Ieong; Lesesvre, Didier

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1093/qmath/haab065

Title :

Quadratic Twists of Central Values For GL(3)

Author(s) :

Kuan, Chan Ieong [Auteur]
Sun Yat-sen University [Guangzhou] [SYSU]
Lesesvre, Didier [Auteur]

Université de Lille

Journal title :

Quarterly Journal of Mathematics

Pages :

991-1034

Publisher :

Oxford University Press (OUP)

Publication date :

2022-09-01

ISSN :

0033-5606

HAL domain(s) :

Mathématiques [math]/Théorie des nombres [math.NT]

English abstract : [en]

Abstract We prove that a cuspidal automorphic representation of $\mathrm{GL}(3)$ over any number field is determined by the quadratic twists of its central value. In the case π is not a Gelbart–Jacquet lift, the result is ...
Show more >Abstract We prove that a cuspidal automorphic representation of $\mathrm{GL}(3)$ over any number field is determined by the quadratic twists of its central value. In the case π is not a Gelbart–Jacquet lift, the result is conditional on the analytic behavior of a certain Euler product. We deduce the nonvanishing of infinitely many quadratic twists of central values. This generalizes a result of Chinta and Diaconu that was valid only over Q and explored only for Gelbart–Jacquet lifts.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2003.06645
Open access
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