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 stablecase.