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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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