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

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.

minor revision; 48 pages; to appear in Annals of Mathematics

References in corpus (3)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• A Theorem on GL(n) a la Tchebotarev

Cited by in corpus (3)

• Spectral aspect subconvex bounds for ${\mathrm{U}}_{n+1}\times {\mathrm{U}}_n$
• Isolation of the Cuspidal Spectrum: the Function Field Case
• Square root $p$-adic $L$-functions, I: Construction of a one-variable measure