Menon-type identities concerning additive characters

TL;DR

This paper generalizes Menon-type identities involving additive characters of the group Z_n using convolutional identities, and explores related formulas for Ramanujan sums and other applications.

Contribution

It introduces a new approach based on convolutional identities to generalize Menon-type identities involving additive characters.

Findings

Generalized Menon-type identities for additive characters

Derived formulas for Ramanujan sums

Presented applications of the new identities

Abstract

By considering even functions (mod $n$) we generalize a Menon-type identity by Li and Kim involving additive characters of the group ${\Bbb Z}_n$. We use a different approach, based on certain convolutional identities. Some other applications, including related formulas for Ramanujan sums, are discussed, as well.