{
  "id": "1205.3937",
  "version": "v4",
  "published": "2012-05-17T14:19:47.000Z",
  "updated": "2012-08-03T13:30:52.000Z",
  "title": "Improved bounds on the set A(A+1)",
  "authors": [
    "Timothy G. F. Jones",
    "Oliver Roche-Newton"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a subset A of a field F, write A(A + 1) for the set {a(b + 1):a,b\\in A}. We establish new estimates on the size of A(A+1) in the case where F is either a finite field of prime order, or the real line. In the finite field case we show that A(A+1) is of cardinality at least C|A|^{57/56-o(1)} for some absolute constant C, so long as |A| < p^{1/2}. In the real case we show that the cardinality is at least C|A|^{24/19-o(1)}. These improve on the previously best-known exponents of 106/105-o(1) and 5/4 respectively.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-08-03T13:30:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field case",
      "best-known exponents",
      "real line",
      "cardinality",
      "prime order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3937J"
    }
  }
}