{
  "id": "math/0503304",
  "version": "v1",
  "published": "2005-03-15T15:48:47.000Z",
  "updated": "2005-03-15T15:48:47.000Z",
  "title": "On a number of rational points on a convex curve",
  "authors": [
    "Fedor V. Petrov"
  ],
  "comment": "8 pages, submitted to FAA",
  "categories": [
    "math.NT",
    "math.MG"
  ],
  "abstract": "Let $\\gamma$ be a bounded convex curve on a plane. Then $\\sharp (\\gamma\\cap (\\Z/n)^2)=o(n^{2/3})$. It streghtens the classical result of Jarn\\'\\i k (an upper estimate $O(n^{2/3})$) and disproves a conjecture of Vershik on existence of the so-called {\\it universal Jarn\\'\\i k curve}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-15T15:48:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H06"
    ],
    "keywords": [
      "rational points",
      "bounded convex curve",
      "upper estimate",
      "classical result",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3304P"
    }
  }
}