Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2019-12-16 DOI:10.4007/annals.2021.194.2.5

Raphael Beuzart-Plessis, Yifeng Liu, Wei Zhang, Xinwen Zhu

引用次数: 22

Abstract

We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of the global Gan--Gross--Prasad conjecture and its refinement Ichino--Ikeda conjecture for $\mathrm{U}(n)\times\mathrm{U}(n+1)$ in the stable case.

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尖谱的分离及其在Gan–Gross–Prasad猜想中的应用

我们介绍了一种分离痕量公式光谱侧成分的新技术。将其应用于Jacquet-Rallis相对迹公式，在稳定情况下，我们完成了$\mathrm{U}（n）\times\mathrm{U}的全局Gan-Gross-Prasad猜想及其改进Ichino-Ikeda猜想的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.