A generalization of Tóth identity involving a Dirichlet character in $\mathbb{F}_q[T]$

Esrafil Ali Molla                <meta name=

2024/104/1-2 (3) — DOI: 10.5486/PMD.2024.9604 — pp. 67-88

A generalization of Tóth identity involving a Dirichlet character in $\mathbb{F}_q[T]$

Authors: Esrafil Ali Molla and Subha Sarkar

Abstract:

Let $\mathbb{A}=\mathbb{F}_q[T]$ be the polynomial ring over the finite field $\mathbb{F}_q$. In this article, we prove a generalization of Tóth identity to $\mathbb{A}$ involving arithmetical functions, multiplicative and additive characters.

Keywords: Menon's identity, Dirichlet character, additive character, arithmetic function, divisor function, Euler's totient function, Möbius function

Mathematics Subject Classification: 11T55, 11A07, 11A25