|DATE||November 09 (Fri), 2018|
|TITLE||Fourier-Jacobi period and critical central $L$-value|
|ABSTRACT||The Gan-Gross-Prasad conjecture predicts that the non-vanishing of certain periods is equivalent to the non-vanishing of certain central value of some $L$-function. There are two types of periods: Bessel period, Fourier-Jacobi(FJ) period. Bessel period is period of automorphic forms on orthogonal group or hermitian unitary group and FJ period is period on symplectic and metaplectic group or skew hermitian unitary group. In a seminal paper of Wei Zhang (2014. Ann. of Math), he proved Bessel case for unitary group and thereafter Hang Xue proved FJ-case for unitary group in a similar way. But both results are under some local restrictions to apply relative trace formula.
In this talk, we prove one direction of the FJ case for unitary group without local restriction. This is a joint work with Hiraku Atobe.