참석 방법: 아래 줌 링크 이용

https://cnrs.zoom.us/j/95421205116?pwd=h09AKYQPbXmECgcDFam7WYoWzMoDuD.1

웹사이트: https://www.math.u-bordeaux.fr/~pthieull/LIA/webinars_NT.html

Speaker:  Paul Boisseau (Max Planck Institute for Mathematics Bonn)

Title: Non-tempered Gan-Gross-Prasad conjecture for general linear groups and residues of zeta integrals

Abstract:  The conjectures of Gan, Gross, and Prasad relate the periods of cuspidal automorphic forms on classical groups to the central values of certain L-functions. Recently, the three authors gave a generalization of these statements for the periods of non-tempered forms. In the case of general linear groups, their conjecture extends the results of Jacquet, Piatetskii-Shapiro, and Shalika on the Rankin-Selberg period to the non-generic spectrum.

In this talk, I will explain how to regularize this integral and show that it indeed computes the special values of L-functions predicted by Gan, Gross, and Prasad. The strategy relies on the observation that the residues of Rankin-Selberg Zeta integrals produce periods of non-generic forms. This same method also allows for the proof of an important part of the local version of the conjecture, completing the works of K.Y. Chan, C. Chen, and R. Chen.