{
  "id": "2002.06221",
  "version": "v1",
  "published": "2020-02-14T19:17:36.000Z",
  "updated": "2020-02-14T19:17:36.000Z",
  "title": "A Khintchine type theorem for affine subspaces",
  "authors": [
    "Daniel C. Alvey"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that affine subspaces of Euclidean space are of Khintchine type for divergence under certain multiplicative Diophantine conditions on the parametrizing matrix. This provides evidence towards the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence, or that Khintchine's theorem still holds when restricted to the subspace. This result is proved as a special case of a more general Hausdorff measure result from which the Hausdorff dimension of W(\\tau) intersected with an appropriate subspace is also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-14T19:17:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine subspaces",
      "khintchine type theorem",
      "euclidean space",
      "general hausdorff measure result",
      "multiplicative diophantine conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}