{
  "id": "1809.03134",
  "version": "v1",
  "published": "2018-09-10T04:43:39.000Z",
  "updated": "2018-09-10T04:43:39.000Z",
  "title": "The error term in the prime number theorem",
  "authors": [
    "Dave Platt",
    "Tim Trudgian"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We make explicit a theorem of Pintz concerning the error term in the prime number theorem. This gives an improved version of the prime number theorem with error term roughly square-root of that which was previously known. We apply this to a long-standing problem concerning an inequality studied by Ramanujan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T04:43:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11N56"
    ],
    "keywords": [
      "prime number theorem",
      "error term roughly square-root",
      "long-standing problem",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}