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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.13132 |
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Table of Contents:
- In this article, we compute the Gan-Gross-Prasad period integral of Klingen Eisenstein series over the unitary group $\mathrm{U}(m+1, n+1)$ with a cuspidal automorphic form over $\mathrm{U}(m+1, n)$, 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 $\mathrm{U}(m,n) \times \mathrm{U}(m+1, n)$. 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.