Automorphic period and the central value of Rankin--Selberg L-function

TL;DR

This paper proves a refined version of the global Gan-Gross-Prasad conjecture for unitary groups, linking automorphic periods to central L-values under certain local assumptions.

Contribution

It provides a significant advancement by confirming a refined conjecture under specific local conditions, assuming properties of L-packets and parts of the local conjecture.

Findings

Refinement of the global Gan-Gross-Prasad conjecture proved

Automorphic periods linked to central L-values for unitary groups

Conditional results based on local properties and conjectures

Abstract

We prove a refinement of the global Gan-Gross-Prasad conjecture proposed by Ichino-Ikeda and N. Harris for unitary groups under some local conditions. We need to assume some expected properties of L-packets and some part of the local Gan-Gross-Prasad conjecture.