ScholarLens Back to search
1991•Illinois Journal of MathematicsRequires access

A note on Ramanujan coefficients of arithmetical functions

Paolo Codecà

Open publisher page 0 citations

Abstract

In this paper we study a problem related to Ramanujan's expansions of multiplicative functions also considered by H.Delange in 1984.We prove the existence of the mean value of certain arithmetical convolutions and also obtain its integral representation.This gives the possibility of computing immediately the Ramanujan coefficients of the arithmetical functions involved. In this way we obtain a short proof of Delange's theorem.We also obtain a new summability result.

About this research paper

What this paper is about

In this paper we study a problem related to Ramanujan's expansions of multiplicative functions also considered by H.Delange in 1984.We prove the existence of the mean value of certain arithmetical convolutions and also obtain its integral representation.This gives the possibility of computing immediately the Ramanujan coefficients of the arithmetical functions involved. In this way we obtain a short proof of Delange's theorem.We also obtain a new summability result.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

In this paper we study a problem related to Ramanujan's expansions of multiplicative functions also considered by H.Delange in 1984.We prove the existence of the mean value of certain arithmetical convolutions and also obtain its integral representation.This gives the possibility of computing immediately the Ramanujan coefficients of the arithmetical functions involved. In this way we obtain a short proof of Delange's theorem.We also obtain a new summability result.

Key concepts: Arithmetic function, Mathematics, Ramanujan's sum, Pure mathematics, Algebra over a field, Discrete mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A note on Ramanujan coefficients of arithmetical functions — Research Paper | ScholarLens