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

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