On the refined Gan-Gross-Prasad conjecture for cusp forms of GSp(4)

Abstract

We prove a conjectural formula relating the Bessel period of certain automorphic forms on ${\mathrm{GSp}}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups $(\SO(5), \SO(2))$. The conjecture has been previously proved for certain automorphic forms on $\mathrm{GS}{\mathrm{p}}_4$ from lifts. In this paper, we extend the formula to Siegel modular forms of $\Sp_4(\bZ)$.

arXiv commentfix constant 1/8; discuss the global L-function. arXiv admin note: text overlap with arXiv:1510.07334