## Isolation of cuspidal spectrum, with application to the Gan-Gross-Prasad conjecture.(English)Zbl 07395719

Summary: 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.

### MSC:

 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11F70 Representation-theoretic methods; automorphic representations over local and global fields 11F72 Spectral theory; trace formulas (e.g., that of Selberg)
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