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The mean value of Hardy sums over short intervals

Published online by Cambridge University Press:  23 July 2007

Zhefeng Xu  and
Wenpeng Zhang
Zhefeng Xu
Affiliation:
Department of Mathematics, Northwest University, Xi'an, Shaanxi, People's Republic of China (zfxu@nwu.edu.cn)
Wenpeng Zhang
Affiliation:
Department of Mathematics, Northwest University, Xi'an, Shaanxi, People's Republic of China (zfxu@nwu.edu.cn)
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Abstract

The main purpose of this paper is to study the mean value properties of certain Hardy sums over a short interval by using the mean-value theorems of the Dirichlet $L$-functions. Our main result is a mean-value formula for these sums.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 4 , August 2007 , pp. 885 - 894
Copyright
2007 Royal Society of Edinburgh

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