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

TL;DR

This paper proves a formula linking Bessel periods of automorphic forms on GSp(4) to central L-values, extending previous results to Siegel modular forms and supporting the refined Gan-Gross-Prasad conjecture.

Contribution

It extends the refined Gan-Gross-Prasad conjecture to include Siegel modular forms of Sp(4), broadening the scope of the conjecture's validation.

Findings

Established the conjectural formula for a broader class of automorphic forms.

Extended the validity of the refined Gan-Gross-Prasad conjecture.

Connected Bessel periods with central L-values for Siegel modular forms.

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 $\mathrm{GSp_4}$ from lifts. In this paper, we extend the formula to Siegel modular forms of $\Sp_4(\bZ)$.