The second and fourth moments of theta functions at their central point

JOURNAL OF NUMBER THEORY

卷:133

Article

Louboutin, Stephane R.¹  Munsch, Marc¹ 

[1] Inst Math Luminy, UMR 6206, F-13288 Marseille 9, France

关键词: Dirichlet characters;    Theta functions;    Mean values;   

DOI  :  10.1016/j.jnt.2012.09.016

来源: Elsevier

【 摘 要 】

Let chi range over the (p - 1)/2 even Dirichlet characters mod p >= 3, a prime. Let theta(x, chi) be the associated theta series. It is known that the square mean value of theta(1, chi) is asymptotic to p(3/2)/4 root 2 as p goes to infinity. We prove that the fourth mean value of theta(1, chi) is asymptotic to 3/16 pi p(2) log p as p goes to infinity. We give similar results for mean values of odd Dirichlet characters mod p. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free