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arXiv · 1511.02221

On correlations of certain multiplicative functions

R. Balasubramanian·Sumit Giri·Priyamvad Srivastav
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Abstract

In this paper, we study sums of shifted products $\sum\limits_{n \leq x} F(n) G(n-h)$ for any $|h| \leq x/2$ and arithmetic functions $F=f*1$ and $G=g*1$, with $f$ and $g$ small. We obtain asymptotic formula for different orders of magnitude of $f$ and $g$. We also provide asymptotic formula for sums of the type $\sum\limits_{n \leq x} μ^2(n) G(n-h)$, where $G=g*1$ and $g$ is small. For small order of magnitudes of $f$ and $g$, we improve the error terms and make them independent of $h$.

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R. Balasubramanian, Sumit Giri, Priyamvad Srivastav. 2016-09-27. On correlations of certain multiplicative functions. https://arxiv.org/abs/1511.02221

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