{
  "id": "1205.5041",
  "version": "v1",
  "published": "2012-05-22T20:14:37.000Z",
  "updated": "2012-05-22T20:14:37.000Z",
  "title": "Simultaneous approximation to a real number and to its cube",
  "authors": [
    "Stéphane Lozier",
    "Damien Roy"
  ],
  "comment": "32 pages, to appear in Acta Arithmetica",
  "journal": "Acta Arithmetica, vol.156 (2012), 39-73",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is known that, for each real number x such that 1,x,x^2 are linearly independent over Q, the uniform exponent of simultaneous approximation to (1,x,x^2) by rational numbers is at most (sqrt{5}-1)/2 (approximately 0.618) and that this upper bound is best possible. In this paper, we study the analogous problem for Q-linearly independent triples (1,x,x^3), and show that, for these, the uniform exponent of simultaneous approximation by rational numbers is at most 2(9+sqrt{11})/35 (approximately 0.7038). We also establish general properties of the sequence of minimal points attached to such triples that are valid for smaller values of the exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-22T20:14:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J13",
      "11J04",
      "11J82"
    ],
    "keywords": [
      "simultaneous approximation",
      "real number",
      "uniform exponent",
      "rational numbers",
      "smaller values"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5041L"
    }
  }
}