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

Haiyan Wang — 2013

Acta Arithmetica

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 D ₁ ( x ; Z F ) by using Ivić’s large value arguments and other techniques.

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