{
  "id": "2203.04242",
  "version": "v1",
  "published": "2022-03-08T18:02:59.000Z",
  "updated": "2022-03-08T18:02:59.000Z",
  "title": "On geometry of simultaneous approximation to three real numbers",
  "authors": [
    "Antoine Marnat",
    "Nikolay Moshchevitin"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "Considering simultaneous approximation to three numbers, we study the geometry of the sequence of best approximations. We provide a sharper lower bound for the ratio between ordinary and uniform exponent of Diophantine approximation, optimal in terms of this geometry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-08T18:02:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real numbers",
      "sharper lower bound",
      "uniform exponent",
      "best approximations",
      "diophantine approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}