{
  "id": "1901.06160",
  "version": "v1",
  "published": "2019-01-18T10:09:35.000Z",
  "updated": "2019-01-18T10:09:35.000Z",
  "title": "Asymptotic of some sums",
  "authors": [
    "Victor Leonidovich Volfson"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The paper compares the asymptotic of the expressions $\\frac {1} {x} \\sum\\limits_{n \\leq x} {f(n)}$ and $\\sum\\limits_{n \\leq x} {\\frac {f(n)} {n}}$, $\\frac {1} {x} \\sum\\limits_{p \\leq x} {f(p)}$ and $\\sum\\limits_{p \\leq x} {\\frac {f(p)} {p}}$. The asymptotic of sums $\\sum\\limits_{n \\leq x} {\\frac {f(n)} {n}}$ and $\\sum\\limits_{p \\leq x} {\\frac {f(p)} {p}}$ ($n,p$ - respectively, positive and prime numbers) are determined if the asymptotic of sums are known, respectively: $\\sum\\limits_{n \\leq x} {f(n)}$,$\\sum\\limits_{p \\leq x} {f(p)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-18T10:09:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37"
    ],
    "keywords": [
      "asymptotic",
      "prime numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}