An average of generalized Dedekind sums

JOURNAL OF NUMBER THEORY

卷:212

Article

Dillon, Travis¹  Gaston, Stephanie² 

[1] Lawrence Univ, Appleton, WI 54912 USA

[2] Calif State Univ Dominguez Hills, Carson, CA USA

关键词: Dedekind sums;    Dirichlet characters;    Fourier transform;   

DOI  :  10.1016/j.jnt.2019.11.008

来源: Elsevier

【 摘 要 】

We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By calculating the Fourier transform of this generalized Dedekind sum, we obtain an explicit formula for its second moment. Finally, we derive upper and lower bounds for the second moment with nearly identical orders of magnitude. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free