{
  "id": "1811.01654",
  "version": "v1",
  "published": "2018-11-05T13:01:40.000Z",
  "updated": "2018-11-05T13:01:40.000Z",
  "title": "Ramanujan expansions of arithmetic functions of several variables over $\\mathbb{F}_{q}[T]$",
  "authors": [
    "Tianfang Qi",
    "Su Hu"
  ],
  "categories": [
    "math.NT"
  ],
  "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 the arithmetic functions of 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T13:01:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T55",
      "11T24",
      "11L05"
    ],
    "keywords": [
      "arithmetic functions",
      "ramanujan expansions",
      "unitary polynomial ramanujan sums",
      "finite field",
      "monic polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}