Ramanujan expansions of arithmetic functions of several variables over ${\mathbb{F}}_q[T]$

Abstract

Let $\mathbb{A}={\mathbb{F}}_q[T]$ be the polynomial ring over finite field ${\mathbb{F}}_q$, and ${\mathbb{A}}_{+}$ be the set of monic polynomials in $\mathbb{A}$. In this paper, we show that a large class of arithmetic functions in multi-variables over ${\mathbb{A}}_{+}$ can be expanded through the polynomial Ramanujan sums and the unitary polynomial Ramanujan sums. These are analogues of classical results over $\mathbb{N}$ by Winter, Delange and Tóth.

27 pages

References in corpus (1)

• Ramanujan expansions of arithmetic functions of several variables