{
  "id": "1405.1187",
  "version": "v2",
  "published": "2014-05-06T08:25:31.000Z",
  "updated": "2015-03-10T11:53:20.000Z",
  "title": "A note on product sets of rationals",
  "authors": [
    "Javier Cilleruelo"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Bourgain, Konyagin and Shparlinski obtained a lower bound for the size of the product set AB when A and B are sets of positive rational numbers with numerator and denominator less or equal than Q. We extend and slightly improve that lower bound using a di?erent approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-06T08:25:31.000Z",
      "abstract": "Bourgain, Konyagin and Shparlinski obtained a lower bound for the size of the product set AB when A,B are subsets of the set of the Farey fractions F_Q. We extend and slightly improve that lower bound using a different approach. We also give lower and upper bounds for the minimum value of |AA|/|A|^2 and |A/A|/|A|^2 when A is a subset of {1,...,Q}.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-10T11:53:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "product set ab",
      "farey fractions",
      "minimum value",
      "upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.1187C"
    }
  }
}