{
  "id": "1401.2689",
  "version": "v2",
  "published": "2014-01-13T00:47:15.000Z",
  "updated": "2014-10-17T01:59:44.000Z",
  "title": "Updating the error term in the prime number theorem",
  "authors": [
    "Tim Trudgian"
  ],
  "comment": "I wish to thank MG Johnson, RJ Harris, PM Siddle, and NM Lyon, all of whom enabled me to work two extra days on this article; 13 pages; to appear in Ramanujan J",
  "categories": [
    "math.NT"
  ],
  "abstract": "An improved estimate is given for $|\\theta(x) -x|$, where $\\theta(x) = \\sum_{p\\leq x} \\log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the third to a conjecture by C. Pomerance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-13T00:47:15.000Z",
      "comment": "I wish to thank MG Johnson, RJ Harris, PM Siddle, and NM Lyon, all of whom enabled me to work two extra days on this article",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-17T01:59:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N27",
      "11M26"
    ],
    "keywords": [
      "prime number theorem",
      "error term",
      "arithmetic progressions",
      "short intervals",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2689T"
    }
  }
}