{
  "id": "2310.01561",
  "version": "v1",
  "published": "2023-10-02T18:53:22.000Z",
  "updated": "2023-10-02T18:53:22.000Z",
  "title": "A note on the quality of simultaneous Diophantine approximations obtained by the LLL algorithm",
  "authors": [
    "Machiel van Frankenhuijsen",
    "Edward K. Voskanian"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1982, A. K. Lenstra, H. W. Lenstra, and L. Lov\\'asz introduced the first polynomial-time method to factor a nonzero polynomial $f \\in \\mathbb{Q}[x]$ into irreducible factors. This algorithm, now commonly referred to as the LLL Algorithm, can also be applied to compute simultaneous Diophantine approximations. We present a significant improvement of a result by Bosma and Smeets on the quality of simultaneous Diophantine approximations achieved by the LLL Algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-02T18:53:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J99"
    ],
    "keywords": [
      "simultaneous diophantine approximations",
      "lll algorithm",
      "first polynomial-time method",
      "nonzero polynomial",
      "significant improvement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}