Fourier–Jacobi periods and the central value of Rankin–Selberg L-functions

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Abstract

In this paper, we propose a conjectural formula, relating the Fourier–Jacobi periods of automorphic forms on U(n)×U(n) and the central value of some Rankin–Selberg L-function. This can be viewed as a refinement of the Gan–Gross–Prasad conjecture for unitary groups. We then use the relative trace formula technique to prove this conjectural formula in some cases. We also have give applications to the conjecture of Ichino–Ikeda and N. Harris on the Bessel period of automorphic forms on unitary groups.

Original languageEnglish (US)
Pages (from-to)547-633
Number of pages87
JournalIsrael Journal of Mathematics
Volume212
Issue number2
DOIs
StatePublished - May 1 2016
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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