{
  "id": "2502.08408",
  "version": "v1",
  "published": "2025-02-12T13:49:23.000Z",
  "updated": "2025-02-12T13:49:23.000Z",
  "title": "Lüroth Expansions in Diophantine Approximation: Metric Properties and Conjectures",
  "authors": [
    "Ying Wai Lee"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper focuses on the metric properties of L\\\"uroth well approximable numbers, studying analogous of classical results, namely the Khintchine Theorem, the Jarn\\'ik--Besicovitch Theorem, and the result of Dodson. A supplementary proof is provided for a measure-theoretic statement originally proposed by Tan--Zhou. The Beresnevich--Velani Mass Transference Principle is applied to extend a dimensional result of Cao--Wu--Zhang. A counterexample is constructed, leading to a revision of a conjecture by Tan--Zhou concerning dimension, along with a partial result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-12T13:49:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric properties",
      "lüroth expansions",
      "diophantine approximation",
      "conjecture",
      "beresnevich-velani mass transference principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}