Refined Global Gan–gross–prasad Conjecture for Fourier–jacobi Periods on Symplectic Groups
نویسنده
چکیده
In this paper, we propose a conjectural identity between the Fourier–Jacobi periods on symplectic groups and the central value of certain Rankin–Selberg L-functions. This identity can be viewed as a refinement to the global Gan–Gross–Prasad conjecture for Sp(2n)×Mp(2m). To support this conjectural identity, we show that when n = m and n = m±1, it can be deduced from the Ichino–Ikeda’s conjecture in some cases via theta correspondences. As a corollary, the conjectural identity holds when n = m = 1 or when n = 2, m = 1 and the automorphic representation on the bigger group is endoscopic.
منابع مشابه
Fourier–jacobi Periods and the Central Value of Rankin–selberg L-functions
1.1. The refined Gan–Gross–Prasad conjecture. In this paper, as a sequel of [Xue14], we formulate a refinement to the global Gan–Gross–Prasad conjecture for the Fourier–Jacobi periods on U(n) × U(n) and prove it under some local conditions, assuming some expected properties of the L-packets and some parts of the local Gan–Gross–Prasad conjecture. This refinement is modeled on some recent work o...
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