{
  "id": "1708.02874",
  "version": "v1",
  "published": "2017-08-09T15:21:50.000Z",
  "updated": "2017-08-09T15:21:50.000Z",
  "title": "Khintchine's Theorem with random fractions",
  "authors": [
    "Felipe A. Ramírez"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a version of Khintchine's Theorem for approximations by rational numbers whose numerators have been randomly chosen, and we explore the extent to which its monotonicity assumption can be removed. This leads to a natural question analogous to the Duffin-Schaeffer Conjecture in this setting, and several other related questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-09T15:21:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "khintchines theorem",
      "random fractions",
      "duffin-schaeffer conjecture",
      "monotonicity assumption",
      "rational numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}