The global Gan-Gross-Prasad conjecture for unitary groups. II. From Eisenstein series to Bessel periods

TL;DR

This paper extends the global Gan-Gross-Prasad and Ichino-Ikeda conjectures to Eisenstein series on unitary groups, using trace formulas and relative characters, and proves these conjectures for Bessel periods.

Contribution

It introduces a novel approach connecting Eisenstein series and Bessel periods via trace formulas and relative characters, advancing the understanding of these conjectures.

Findings

Proved the extended Gan-Gross-Prasad and Ichino-Ikeda conjectures for certain Eisenstein series.

Expressed spectral contributions in trace formulas through integrals of relative characters.

Established the conjectures for Bessel periods of unitary groups.

Abstract

We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$. Our theorems are based on a comparison of the Jacquet-Rallis trace formulas. A new point is the expression of some interesting spectral contributions in these formulas in terms of integrals of relative characters. As an application of our mains theorems, we prove the global Gan-Gross-Prasad and the Ichino-Ikeda conjecture for Bessel periods of unitary groups.