The Dirichlet divisor problem over square-free integers and unitary convolutions

André Pierro de Camargo
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 549–556
DOI: 10.7546/nntdm.2023.29.3.549-556
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Authors and affiliations

André Pierro de Camargo
Federal University of the ABC Region, Brazil


We obtain an asymptotic formula for the sum \tilde{D}_2 of the divisors of all square-free integers less than or equal to x, with error term O(x^{1/2 + \epsilon}). This improves the error term O(x^{3/4 + \epsilon}) presented in [7] obtained via analytical methods. Our approach is elementary and it is based on the connections between the function \tilde{D}_2 and unitary convolutions.


  • Dirichlet divisor problem
  • Square-free integers
  • Unitary convolutions

2020 Mathematics Subject Classification

  • 11N56
  • 11N37


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Manuscript history

  • Received: 11 April 2023
  • Revised: 23 May 2023
  • Accepted: 24 July 2023
  • Online First: 27 July 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Camargo, A. P. (2023). The Dirichlet divisor problem over square-free integers and unitary convolutions. Notes on Number Theory and Discrete Mathematics, 29(3), 549-556, DOI: 10.7546/nntdm.2023.29.3.549-556.

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