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

Tianfang Qi; Su Hu

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arXiv · 1811.01654

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

Tianfang Qi·Su Hu

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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 T\'oth.

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Tianfang Qi, Su Hu. 2018-11-05. Ramanujan expansions of arithmetic functions of several variables over $\mathbb{F}_{q}[T]$. https://arxiv.org/abs/1811.01654

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