|DATE||November 09 (Fri), 2018|
|TITLE||Fourier-Jacobi period and critical central $L$-value|
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.