D. Bhattacharjee

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 1, Pages 32–44

DOI: 10.7546/nntdm.2021.27.1.32-44

**Full paper (PDF, 600 Kb)**

## Details

### Authors and affiliations

D. Bhattacharjee

*Department of Mathematics, North-Eastern Hill University
Permanent Campus, Shillong-793022, India
*

### Abstract

In this paper by an arithmetic function we shall mean a real-valued function on the set of positive integers. We recall the definitions of some common arithmetic convolutions. We also recall the definitions of a multiplicative function, a generalized multiplicative function (or briefly a * GM*-function), an additive function and a generalized additive function (or briefly a

*-function). We shall study in details some properties of*

**GA***-functions as well as*

**GM***-functions using some particular arithmetic convolutions namely the Narkiewicz’s*

**GA***A*-product and the author’s

*B*-product. We conclude our discussion with some examples.

### Keywords

- Arithmetic function
- Multiplicative function
- Arithmetic convolution
- Dirichlet convolution
- Narkiewicz’s
*A*-product *B*-product- Multiplicative
*B*-product -function**GA**-function**GM**

### 2010 Mathematics Subject Classification

- 11A25

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## Cite this paper

Bhattacharjee, D. (2021). A study on some generalized multiplicative and generalized additive arithmetic functions. *Notes on Number Theory and Discrete Mathematics*, 27(1), 32-44, DOI: 10.7546/nntdm.2021.27.1.32-44.