{
  "id": "2304.02566",
  "version": "v1",
  "published": "2023-04-05T16:38:00.000Z",
  "updated": "2023-04-05T16:38:00.000Z",
  "title": "Sums of Reciprocals of Fractional Parts II",
  "authors": [
    "Reynold Fregoli"
  ],
  "comment": "- Appendix by Michael Bj\\\"orklund, Reynold Fregoli, and Alexander Gorodnik - This is the NEW VERSION of a paper entitled Sums of Reciprocals of Fractional Parts over Aligned Boxes (identifier arXiv:2101.11094) by the same author. The previous version will not be published",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we generalise a result of Kruse (1964) concerning the almost sure order of magnitude of sums of reciprocals of fractional parts, thereby solving a conjecture posed by Beresnevich, Haynes, and Velani. The methods are based both on the geometry of numbers and probability theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-05T16:38:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P21",
      "11H16",
      "11J13"
    ],
    "keywords": [
      "fractional parts",
      "reciprocals",
      "sure order",
      "probability theory",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}