Abstract
In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups \(U_{n}\times U_{n+1}\) in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain cuspidal data, called ∗-regular, to the Jacquet-Rallis trace formula for linear groups. We offer two different computations of these contributions: one, based on truncation, is expressed in terms of regularized Rankin-Selberg periods of Eisenstein series and Flicker-Rallis intertwining periods introduced by Jacquet-Lapid-Rogawski. The other, built upon Zeta integrals, is expressed in terms of functionals on the Whittaker model. A direct proof of the equality between the two expressions is also given. Finally several useful auxiliary results about the spectral expansion of the Jacquet-Rallis trace formula are provided.
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Beuzart-Plessis, R., Chaudouard, PH. & Zydor, M. The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case. Publ.math.IHES 135, 183–336 (2022). https://doi.org/10.1007/s10240-021-00129-1
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DOI: https://doi.org/10.1007/s10240-021-00129-1