{
  "id": "0802.1910",
  "version": "v1",
  "published": "2008-02-13T20:21:07.000Z",
  "updated": "2008-02-13T20:21:07.000Z",
  "title": "On a theorem of V. Bernik in the metrical theory of Diophantine approximation",
  "authors": [
    "Victor Beresnevich"
  ],
  "comment": "11 pages",
  "journal": "Acta Arith. 117 (2005), no. 1, 71-80",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "This paper goes back to a famous problem of Mahler in metrical Diophantine approximation. The problem has been settled by Sprindzuk and subsequently improved by Alan Baker and Vasili Bernik. In particular, Bernik's result establishes a convergence Khintchine type theorem for Diophantine approximation by polynomials, that is it allows arbitrary monotonic error of approximation. In the present paper the monotonicity assumption is completely removed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-13T20:21:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J13",
      "11J83",
      "11K60"
    ],
    "keywords": [
      "metrical theory",
      "convergence khintchine type theorem",
      "berniks result establishes",
      "arbitrary monotonic error",
      "alan baker"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.1910B"
    }
  }
}