{
  "id": "2405.11274",
  "version": "v1",
  "published": "2024-05-18T12:18:20.000Z",
  "updated": "2024-05-18T12:18:20.000Z",
  "title": "Hausdorff dimension of singular vectors in function fields",
  "authors": [
    "Noy Soffer Aranov",
    "Taehyeong Kim"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of $\\varepsilon$-Dirichlet improvable vectors in this setting. This is a function field analogue of the results of Cheung and Chevallier [Duke Math. J. 165 (2016), 2273--2329].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-18T12:18:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "singular vectors",
      "function field analogue",
      "duke math",
      "dirichlet improvable vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}