The Dirichlet divisor problem over square-free integers and unitary convolutions
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Published:2023-07-27
Issue:3
Volume:29
Page:549-556
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ISSN:1310-5132
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Container-title:Notes on Number Theory and Discrete Mathematics
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language:
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Short-container-title:NNTDM
Author:
Camargo André Pierro deORCID,
Abstract
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.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)