{
  "id": "1906.09906",
  "version": "v1",
  "published": "2019-06-18T04:29:17.000Z",
  "updated": "2019-06-18T04:29:17.000Z",
  "title": "On Littlewood's proof of the prime number theorem",
  "authors": [
    "Aleksander Simonič"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note we examine Littlewood's proof of the prime number theorem. We show that this can be extended to provide an equivalence between the prime number theorem and the non-vanishing of Riemann's zeta-function on the one-line. Our approach goes through the theory of almost periodic functions and is self-contained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-18T04:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "42A75"
    ],
    "keywords": [
      "prime number theorem",
      "littlewoods proof",
      "riemanns zeta-function",
      "periodic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}