Automorphic period and the central value of Rankin--Selberg L-function

Abstract

We prove a refinement of the global Gan-Gross-Prasad conjecture proposed by Ichino-Ikeda and N. Harris for unitary groups under some local conditions. We need to assume some expected properties of L-packets and some part of the local Gan-Gross-Prasad conjecture.

v4: Final version, slightly different from the published version. v3: the local result for a split archimedean place; some mistakes/typos corrected; the main result remains

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