Frontiers of Mathematics in China >

2017 , Vol. 12 >Issue 2: 367 - 375

DOI: https://doi.org/10.1007/s11464-016-0547-6

RESEARCH ARTICLE

DDT Theorem over square-free numbers in short interval

  • Bin FENG , 1,2 ,
  • Zhen CUI 1
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  • 1. School of Mathematics Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
  • 2. College of Mathematics and Statistics, Yangtze Normal University, Fuling 408100, China

Received date: 23 Feb 2016

Accepted date: 06 May 2016

Published date: 20 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We study the Cesàro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.

Key words： Selberg-Delang method; arcsine law; square-free number

Cite this article

Bin FENG , Zhen CUI . DDT Theorem over square-free numbers in short interval[J]. Frontiers of Mathematics in China, 2017 , 12(2) : 367 -375 . DOI: 10.1007/s11464-016-0547-6

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