Time: 16:00-17:00, Wednesday, March 5  

Title: On the non-vanishing of central values of Rankin–Selberg L-functions

Speaker: Bin Xu (Sichuan University)

Abstract: In this talk, we introduce an approach to obtaining non-vanishing results for the central values of automorphic L-functions. Specifically, we consider Rankin–Selberg L-functions associated with cuspidal automorphic representations of general linear groups, which parametrize automorphic representations of classical groups. Our method relies on the close connection between automorphic descent constructions and the Gan–Gross–Prasad conjectures. For general-rank cases, we will explain how this approach yields non-vanishing central L-values under certain assumptions. In particular, for some lower-rank cases, we can establish unconditional non-vanishing results for the central L-values of cuspidal automorphic representations twisted by certain characters.