Some asymptotic formulae involving Cohen-Ramanujan expansions

Arya Chandran; K Vishnu Namboothiri

Some asymptotic formulae involving Cohen-Ramanujan expansions

Number Theory 2024-01-02 v2

Authors: Arya Chandran , K Vishnu Namboothiri

Abstract

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.

Keywords

ramanujan identities and series multiplicative functions asymptotic analysis

Cite

@article{arxiv.2303.09363,
  title  = {Some asymptotic formulae involving Cohen-Ramanujan expansions},
  author = {Arya Chandran and K Vishnu Namboothiri},
  journal= {arXiv preprint arXiv:2303.09363},
  year   = {2024}
}

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