Date：April 19th 16:00-17:00

Location：Lecture hall

Abstract：

Spectral reciprocities are equalities between moments of automorphic L-functions in different families. They are powerful tools for the study of the moment problem and the subconvexity problem. The first spectral reciprocity formula is Motohashi's formula, which relates the cubic moment of L-functions for GL_2 with the fourth moment of L-functions for GL_1. The exploitation of this formula (over $\mathbb{Q}$) has led Conrey-Iwaniec and Petrow-Young to the uniform Weyl bound for all Dirichlet L-functions. In this talk, we will present and compare two recent approaches to the general form of Motohashi's formula over arbitrary number fields. Applications, such as the generalization of Petrow-Young's result over totally real number fields, the further generalization to some families of L-functions for PGL_2, and the new error term bound of the Partition function etc., will be discussed as much as time permits.