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Abstract

Let $F$ be a Siegel cusp form of integral weight $k$ on the Siegel modular group $Sp_2(\mathbb{Z})$ of genus $2$. The coefficients of the spinor zeta function $Z_F(s)$ are denoted by $c_n$. Let $D_\rho(x;Z_F)$ be the Riesz mean of $c_n$. Kohnen and Wang obtained the truncated Voronoï-type formula for $D_\rho(x;Z_F)$ under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of $D_\rho(x; Z_F)$, and then derive an asymptotic formula for the $h$th ($h=3,4,5$) power moments of $D_1(x; Z_F)$ by using Ivić's large value arguments and other techniques.