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Research Article | Open Access

On mean square of the error term of a multivariable divisor function

Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
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Abstract

Let τ(n) be the Dirichlet divisor function and k⩾2 be a fixed integer. We give an asymptotic formula of the mean square of

Δk(x)=∑n1,⋯,nk⩽xτ(n1⋯nk)−xkPk(log⁡x).

Keywords

divisor functionmean squareDirichlet series
CLC number: 11N37

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 29197-29219
DOI: 10.3934/math.20241415

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Cite this article:
Guo Z. On mean square of the error term of a multivariable divisor function. AIMS Mathematics, 2024, 9(10): 29197-29219. https://doi.org/10.3934/math.20241415

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Received: 29 August 2024
Revised: 09 October 2024
Accepted: 10 October 2024
Published: 15 October 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)