{
  "id": "2312.02414",
  "version": "v1",
  "published": "2023-12-05T01:08:36.000Z",
  "updated": "2023-12-05T01:08:36.000Z",
  "title": "Bounds on the gaps in Kronecker sequences (and a little bit more)",
  "authors": [
    "Seungki Kim"
  ],
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We provide bounds on the sizes of the gaps -- defined broadly -- in the set $\\{k_1\\vbeta_1 + \\ldots + k_n\\vbeta_n \\mbox{ (mod 1)} : k_i \\in \\Z \\cap (0,Q^\\frac{1}{n}]\\}$ for generic $\\vbeta_1, \\ldots, \\vbeta_n \\in \\R^m$ and all sufficiently large $Q$. We also introduce a related problem in Diophantine approximation, which we believe is of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-05T01:08:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kronecker sequences",
      "little bit",
      "diophantine approximation",
      "independent interest",
      "related problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}