Geodesic
On the spinor zeta functions problem: higher power moments of the Riesz mean
Haiyan Wang1
1 School of Mathematics and Quantitative Economics Shandong University of Finance and Economics Jinan, 250014, P.R. China
Acta Arithmetica, Tome 157 (2013) no. 3, pp. 231-248 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa157-3-2
Keywords: siegel cusp form integral weight siegel modular group mathbb genus coefficients spinor zeta function denoted rho riesz mean kohnen wang obtained truncated vorono type formula rho under ramanujan petersson conjecture paper study higher power moments rho derive asymptotic formula hth power moments using ivi large value arguments other techniques

Haiyan Wang 1

1 School of Mathematics and Quantitative Economics Shandong University of Finance and Economics Jinan, 250014, P.R. China 
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Haiyan Wang. On the spinor zeta functions problem: higher
power moments of the Riesz mean. Acta Arithmetica, Tome 157 (2013) no. 3, pp. 231-248. doi: 10.4064/aa157-3-2

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