Some asymptotic formulae involving Cohen-Ramanujan expansions

2023/03/16 by Arya Chandran, Chandran, Arya, K Vishnu Namboothiri +1
Mathematics · #11A25 #11L03 #11N05 #11N37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2303.09363

openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some necessary and sufficient conditions for the existence of Cohen-Ramanujan expansions for arithmetical functions were provided by these authors in [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 ∑_{n≤ 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.

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