The Gan-Gross-Prasad period of Klingen Eisenstein families over unitary groups

2024/10/17 by Xu, Ruichen
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.13132

Abstract

In this article, we compute the Gan-Gross-Prasad period integral of Klingen Eisenstein series over the unitary group U(m+1, n+1) with a cuspidal automorphic form over U(m+1, n), and show that it is related to certain special Rankin-Selberg L-values. We p-adically interpolate these Gan-Gross-Prasad period integrals as the Klingen Eisenstein series and the cuspidal automorphic form vary in Hida families. As a byproduct, we obtain a p-adic L-function of Rankin-Selberg type over U(m,n) × U(m+1, n). The ultimate motivation is to show the p-primitive property of Klingen Eisenstein series over unitary groups, by computing such Gan-Gross-Prasad period integrals, and this article is a starting point of this project. The p-primitivity of Eisenstein series is an essential property in the automorphic method in Iwasawa theory.

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