{
  "id": "1906.09100",
  "version": "v1",
  "published": "2019-06-21T12:46:30.000Z",
  "updated": "2019-06-21T12:46:30.000Z",
  "title": "Large gaps between sums of two squares",
  "authors": [
    "A. B. Kalmynin",
    "S. V. Konyagin"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathcal S=\\{s_1<s_2<s_3<\\ldots\\}$ be the sequence of all natural numbers which can be represented as a sum of two squares of integers. For $X\\ge2$ we denote by $g(X)$ the largest gap between consecutive elements of $\\mathcal S$ that do not exceed $X$. We prove that for $X \\to +\\infty$ the lower bound $$g(X)\\geq \\left(\\frac{390}{449}-o(1)\\right)\\ln X$$ holds. This estimate is twice the recent estimate by R. Dietmann and C. Elsholtz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-21T12:46:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25"
    ],
    "keywords": [
      "large gaps",
      "natural numbers",
      "largest gap",
      "lower bound",
      "consecutive elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}