# Ramanujan expansions of arithmetic functions of several variables

## TL;DR

This paper extends recent work on Ramanujan expansions to functions of multiple variables, demonstrating parallels between classical and unitary Ramanujan sums in these expansions.

## Contribution

It generalizes existing results on Ramanujan expansions from two-variable functions to functions of several variables, highlighting similarities in properties across different types of sums.

## Key findings

- Extended Ramanujan expansion results to multiple variables
- Identified parallels between classical and unitary Ramanujan sums
- Provided theoretical framework for multi-variable arithmetic functions

## Abstract

We generalize certain recent results of Ushiroya concerning Ramanujan expansions of arithmetic functions of two variables. We also show that some properties on expansions of arithmetic functions of one and several variables using classical and unitary Ramanujan sums, respectively, run parallel.