AUTOMORPHIC PERIOD AND THE CENTRAL VALUE OF RANKIN-SELBERG L-FUNCTION

摘要

In this article, as a sequel of [51], we prove a conjectural refinement of the global Gan-Gross-Prasad conjecture [7] for unitary groups under some local conditions. This refinement is modeled on the pioneering work of Waldspurger [40] on toric periods and the central values of L-functions on GL_2. In an influential paper [23], Ichino and Ikeda first formulated the refinement for orthogonal groups. After the Ichino-Ikeda formulation, R. N. Harris considered the case of unitary groups in his Ph.D. thesis at the University of California, San Diego [21].