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

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.

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