{
  "id": "1511.08070",
  "version": "v1",
  "published": "2015-11-25T14:16:30.000Z",
  "updated": "2015-11-25T14:16:30.000Z",
  "title": "Counting $r$-tuples of positive integers with $k$-wise relatively prime components",
  "authors": [
    "László Tóth"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $r\\ge k\\ge 2$ be fixed positive integers. Let $\\varrho_{r,k}$ denote the characteristic function of the set of $r$-tuples of positive integers with $k$-wise relatively prime components, that is any $k$ of them are relatively prime. We use the convolution method to establish an asymptotic formula for the sum $\\sum_{n_1,\\ldots,n_r\\le x} \\varrho_{r,k}(n_1,\\ldots,n_r)$ by elementary arguments. Our result improves the error term obtained by J. Hu (2013).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-25T14:16:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A05",
      "11A25",
      "11N37"
    ],
    "keywords": [
      "wise relatively prime components",
      "positive integers",
      "characteristic function",
      "convolution method",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}