{
  "id": "1409.1780",
  "version": "v1",
  "published": "2014-09-05T13:09:55.000Z",
  "updated": "2014-09-05T13:09:55.000Z",
  "title": "New bounds for the prime counting function π(x)",
  "authors": [
    "Christian Axler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we establish a number of new estimates concerning the prime counting function \\pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in small intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-05T13:09:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11A41",
      "11B05"
    ],
    "keywords": [
      "prime counting function",
      "small intervals",
      "prime numbers",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.1780A"
    }
  }
}