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# Some asymptotic formulae involving Cohen-Ramanujan expansions

Mar 2023

Some necessary and sufficient conditions for the existence of Cohen-Ramanujanexpansions for arithmetical functions were provided by these authors in[\textit{arXive preprint arXive:2205.08466}, 2022]. Given two arithmeticalfunctions $f$ and $g$ with absolutely convergent Cohen-Ramanujan expansions, wederive an asymptotic formula for $\sum_{n\leq N}f(n)g(n+h)$ where $h$ is afixed positive integer. We also provide Cohen-Ramanujan expansions for certainfunctions to illustrate some of the results we prove consequently.

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