{
  "id": "1110.6864",
  "version": "v1",
  "published": "2011-10-31T17:12:31.000Z",
  "updated": "2011-10-31T17:12:31.000Z",
  "title": "Asymptotics for numbers of line segments and lines in a square grid",
  "authors": [
    "Pentti Haukkanen",
    "Jorma K. Merikoski"
  ],
  "journal": "International Journal of Number Theory 2012",
  "doi": "10.1142/S1793042112500698",
  "categories": [
    "math.NT",
    "cs.IT",
    "math.CO",
    "math.IT"
  ],
  "abstract": "We present an asymptotic formula for the number of line segments connecting q+1 points of an nxn square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case q=2 is so generalized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-31T17:12:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A99",
      "11N37",
      "11P21"
    ],
    "keywords": [
      "asymptotic formula",
      "nxn square grid",
      "sharper formula",
      "riemann hypothesis",
      "well-known case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6864H"
    }
  }
}