A unitary analogy of Friedberg-Jacquet and Guo-Jacquet periods and central values of standard L functions on GL(2n)

 A unitary analogy of Friedberg-Jacquet and Guo-Jacquet periods and central values of standard L functions on GL(2n)

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Jingwei Xiao, Princeton University and IAS

Zoom link:  https://princeton.zoom.us/j/97126136441

Password: the three digit integer that is the cube of the sum of its digits

Let G be a reductive group over a number field F and H a subgroup. Automorphic periods study the integrals of cuspidal automorphic forms on G over H(F)\H(A_F). They are often related to special values of certain L functions. One of the most notable case is when (G,H)=(U(n+1)U(n), U(n)), and these periods are related to central values of Rankin-Selberg L functions on GL(n+1)GL(n). In this talk, I will explain my work in progress with Wei Zhang that studies central values of standard L functions on GL(2n) using (G,H)=(U(2n), U(n)U(n)) and some variants. I shall explain the conjecture and a relative trace formula approach to study it. We prove the required fundamental lemma using a limit of the Jacquet-Rallis fundamental lemma and Hironaka’s characterization of spherical functions on the space of non degenerate Hermitian matrices. Also, the question admits an arithmetic analogy.