Mean Values of the Hardy Sum

WANG Xiao-ying, YUE Xia-xia

doi:10.13371/j.cnki.chin.q.j.m.2017.01.003

Chinese Quarterly Journal of Mathematics >

2017 , Vol. 32 >Issue 1: 16 - 33

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.01.003

Mean Values of the Hardy Sum

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School of Mathematics,Northwest University

WANG Xiao-ying(1964-), female, native of Changwu, Shaanxi, a professor of Northwest University, Ph.D., engages in analytic number theory.

Received date: 2015-11-06

Online published: 2020-10-26

Supported by

Supported by the National Natural Science Foundation of China(11571277)； Supported by the Science and Technology Program of Shaanxi Province(2016GY-077)；

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Abstract

Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H（h,p）=sum(（-1）^{j+1+[（hj）/p]})from （p-1） to （j=1） which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions.

Key words： Dedekind sum; Hardy sum; mean value; Dirichlet L-function

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WANG Xiao-ying, YUE Xia-xia . Mean Values of the Hardy Sum[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(1) : 16 -33 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.01.003

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