On correlations of certain multiplicative functions

Abstract

In this paper, we study sums of shifted products $\sum _{n\le x}F(n)G(n-h)$ for any $|h|\le x/2$ and arithmetic functions $F=f\ast 1$ and $G=g\ast 1$, 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 $\sum _{n\le x}{\mu }^2(n)G(n-h)$, where $G=g\ast 1$ and $g$ is small. For small order of magnitudes of $f$ and $g$, we improve the error terms and make them independent of $h$.

13 pages

References in corpus (2)

• An averaged form of Chowla's conjecture
• On the error term in a Parseval type formula in the theory of Ramanujan expansions