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

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 on $\mathbb{A}$ involving arithmetical functions, multiplicative and additive characters.

18 pages