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 multivariables 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 DOI:
 10.48550/arXiv.1811.01654
 arXiv:
 arXiv:1811.01654
 Bibcode:
 2018arXiv181101654Q
 Keywords:

 Mathematics  Number Theory;
 11T55;
 11T24 (Primary);
 11L05 (Secondary)
 EPrint:
 27 pages