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Seminar
FIELD Mathematics
DATE November 09 (Fri), 2018
TIME 17:00-18:00
PLACE 8309
SPEAKER Jaeho Haan
HOST Haan, Jae-ho
INSTITUTE CMC
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.

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