{
  "id": "1809.06159",
  "version": "v1",
  "published": "2018-09-17T12:37:00.000Z",
  "updated": "2018-09-17T12:37:00.000Z",
  "title": "Diophantine approximation on curves and the distribution of rational points: divergence theory",
  "authors": [
    "V. Beresnevich",
    "R. C. Vaughan",
    "S. Velani",
    "E. Zorin"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we develop a new explicit method to studying rational points near manifolds and obtain optimal lower bounds on the number of rational points of bounded height lying at a given distance from an arbitrary non-degenerate curve. This generalises previous results for analytic non-degenerate curves. Furthermore, the main results are also proved in the inhomogeneous setting. Applications of the main theorem include the Khintchine-Jarn\\'ik type theorem for divergence for arbitrary non-degenerate curve in $\\mathbb{R}^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-17T12:37:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J83",
      "11J13",
      "11K60",
      "11K55"
    ],
    "keywords": [
      "rational points",
      "divergence theory",
      "diophantine approximation",
      "arbitrary non-degenerate curve",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}