Some asymptotic formulae involving Cohen-Ramanujan expansions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909057519976448 |
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| author | Chandran, Arya Namboothiri, K Vishnu |
| author_facet | Chandran, Arya Namboothiri, K Vishnu |
| contents | Some necessary and sufficient conditions for the existence of Cohen-Ramanujan expansions for arithmetical functions were provided by these authors in [\textit{arXive preprint arXive:2205.08466}, 2022]. Given two arithmetical functions $f$ and $g$ with absolutely convergent Cohen-Ramanujan expansions, we derive an asymptotic formula for $\sum_{n\leq N}f(n)g(n+h)$ where $h$ is a fixed positive integer. We also provide Cohen-Ramanujan expansions for certain functions to illustrate some of the results we prove consequently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some asymptotic formulae involving Cohen-Ramanujan expansions Chandran, Arya Namboothiri, K Vishnu Number Theory 11A25, 11L03, 11N05, 11N37 Some necessary and sufficient conditions for the existence of Cohen-Ramanujan expansions for arithmetical functions were provided by these authors in [\textit{arXive preprint arXive:2205.08466}, 2022]. Given two arithmetical functions $f$ and $g$ with absolutely convergent Cohen-Ramanujan expansions, we derive an asymptotic formula for $\sum_{n\leq N}f(n)g(n+h)$ where $h$ is a fixed positive integer. We also provide Cohen-Ramanujan expansions for certain functions to illustrate some of the results we prove consequently. |
| title | Some asymptotic formulae involving Cohen-Ramanujan expansions |
| topic | Number Theory 11A25, 11L03, 11N05, 11N37 |
| url | https://arxiv.org/abs/2303.09363 |