{
  "id": "2201.12162",
  "version": "v1",
  "published": "2022-01-28T14:52:46.000Z",
  "updated": "2022-01-28T14:52:46.000Z",
  "title": "Dirichlet improvability for $S$-numbers",
  "authors": [
    "Sourav Das",
    "Arijit Ganguly"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the problem of improving Dirichlet's theorem of metric Diophantine approximation in the $S$-adic setting. Our approach is based on translation of the problem related to Dirichlet improvability into a dynamical one, and the main technique of our proof is the $S$-adic version of quantitative nondivergence estimate due to D. Y. Kleinbock and G. Tomanov. The main result of this paper can be regarded as the number field version of earlier works of D. Y. Kleinbock and B. Weiss, and of the second named author and Anish Ghosh.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-28T14:52:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet improvability",
      "metric diophantine approximation",
      "number field version",
      "second named author",
      "main technique"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}