Speaker：Lei Zhang（National University of Singapore）

Time：2022-10-27, 15:00

Location：Tencent Meeting ID：587-154-242（No Password）

Abstract:

Fourier coefficients of automorphic forms have many applications in number theory such as counting the number of representations of a natural number as the sum of squares. Guided by the local-global principle, a necessary nonvanishing condition of such Fourier coefficients is determined by the wavefront set of the representations over local fields. In this talk, we use the  local Gan-Gross-Prasad conjecture and consecutive local descent theory to introduce a new invariant associated to the irreducible representations in the generic L-packets, so called arithmetic wavefront sets. And we conjecture that the arithmetic wavefront sets coincide the classical wavefront sets defined by the Harish-Chandra characters. This is a joint work with Dihua Jiang and Dongwen Liu.