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

Haiyan Wang

Haiyan Wang

Acta Arithmetica, Tome 161 (2013), p. 231-248 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2013-01-01

Zbl 1321.11104

EUDML-ID : urn:eudml:doc:279341

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     author = {Haiyan Wang},
     title = {On the spinor zeta functions problem: higher power moments of the Riesz mean},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {231-248},
     zbl = {1321.11104},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-3-2}
}

Haiyan Wang. On the spinor zeta functions problem: higher power moments of the Riesz mean. Acta Arithmetica, Tome 161 (2013) pp. 231-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-3-2/