Mean value of the Hardy sums over short intervals

Lei Liu; Zhefeng Xu; Lei Liu; Zhefeng Xu

doi:10.3934/math.2020356

AIMS Mathematics

2020, Volume 5, Issue 6: 5551-5563. doi: 10.3934/math.2020356

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Research article

Mean value of the Hardy sums over short intervals

Lei Liu ,
Zhefeng Xu ^,

School of Mathematics, Northwest University, Xi’an 710127, Shaanxi, P. R. China

Received: 06 April 2020 Accepted: 22 June 2020 Published: 29 June 2020
MSC : 11F20, 11L40

The main purpose of this paper is using the mean value of Dirichlet L-functions and character sums to study a kind of mean value of the Hardy sums over short intervals, and give some interesting formulae.
- Hardy sum,
- L-functions,
- short intervals,
- character sums,
- mean value
Citation: Lei Liu, Zhefeng Xu. Mean value of the Hardy sums over short intervals[J]. AIMS Mathematics, 2020, 5(6): 5551-5563. doi: 10.3934/math.2020356

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Abstract

The main purpose of this paper is using the mean value of Dirichlet L-functions and character sums to study a kind of mean value of the Hardy sums over short intervals, and give some interesting formulae.

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