On the spinor zeta functions problem: higher power moments of the Riesz mean

• Autorzy: Haiyan Wang
• Języki publikacji: EN

Abstrakty

EN

Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function $Z_F(s)$ are denoted by cₙ. Let $D_ρ(x;Z_F)$ be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for $D_ρ(x;Z_F)$ under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of $D_ρ(x;Z_F)$, and then derive an asymptotic formula for the hth (h=3,4,5) power moments of $D₁(x;Z_F)$ by using Ivić's large value arguments and other techniques.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 157
• Numer: 3
• Strony: 231-248

Daty

wydano

2013

Twórcy

autor

Haiyan Wang

• School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, P.R. China

Identyfikatory

DOI

10.4064/aa157-3-2