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

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

Ann. Math. (2) 194, No. 2, 519-584 (2021).

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)

Keywords:

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