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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 
@article{10_4064_aa157_3_2,
     author = {Haiyan Wang},
     title = {On the spinor zeta functions problem: higher
power moments of the {Riesz} mean},
     journal = {Acta Arithmetica},
     pages = {231--248},
     publisher = {mathdoc},
     volume = {157},
     number = {3},
     year = {2013},
     doi = {10.4064/aa157-3-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa157-3-2/}
}
TY  - JOUR
AU  - Haiyan Wang
TI  - On the spinor zeta functions problem: higher
power moments of the Riesz mean
JO  - Acta Arithmetica
PY  - 2013
SP  - 231
EP  - 248
VL  - 157
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa157-3-2/
DO  - 10.4064/aa157-3-2
LA  - en
ID  - 10_4064_aa157_3_2
ER  - 
%0 Journal Article
%A Haiyan Wang
%T On the spinor zeta functions problem: higher
power moments of the Riesz mean
%J Acta Arithmetica
%D 2013
%P 231-248
%V 157
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa157-3-2/
%R 10.4064/aa157-3-2
%G en
%F 10_4064_aa157_3_2
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. http://geodesic.mathdoc.fr/articles/10.4064/aa157-3-2/

Cité par Sources :