{
  "id": "1404.5163",
  "version": "v2",
  "published": "2014-04-21T10:25:44.000Z",
  "updated": "2014-09-26T12:37:32.000Z",
  "title": "On values of binary quadratic forms at integer points",
  "authors": [
    "Manoj Choudhuri",
    "S. G. Dani"
  ],
  "comment": "20 pages, 3 figures added, Accepted for publication in Mathematical Research Letters",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We obtain estimates for the number of integral solutions in large balls, of inequalities of the form $|Q(x, y)| < \\epsilon$, where $Q$ is an indefinite binary quadratic form, in terms of the Hurwitz continued fraction expansions of the slopes of the lines on which $Q$ vanishes. The method is based on a coding of geodesics on the modular surface via Hurwitz expansions of the endpoints of their lifts in the Poincare half-plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-21T10:25:44.000Z",
      "comment": "18 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-26T12:37:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K60",
      "37A17"
    ],
    "keywords": [
      "integer points",
      "indefinite binary quadratic form",
      "hurwitz continued fraction expansions",
      "large balls",
      "integral solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5163C"
    }
  }
}