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

Raphaël Beuzart-Plessis; Yifeng Liu; Wei Zhang; Xinwen Zhu

doi:https://www.doi.org/10.4007/annals.2021.194.2.5

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

Pages 519-584 from Volume 194 (2021), Issue 2 by Raphaël Beuzart-Plessis, Yifeng Liu, Wei Zhang, Xinwen Zhu

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.

Keywords

Gan--Gross--Prasad conjecture, cuspidal automorphic representations, isolation of spectrum, multipliers, trace formula

Mathematical Subject Classification

Primary 2000: 11F67, 11F70, 11F72

DOI

https://www.doi.org/10.4007/annals.2021.194.2.5

4298750

zbMATH

7395719

Milestones

Received: 17 January 2020
Revised: 17 May 2021
Accepted: 21 May 2021
Published online: 13 August 2021