{
  "id": "1609.07934",
  "version": "v1",
  "published": "2016-09-26T11:48:33.000Z",
  "updated": "2016-09-26T11:48:33.000Z",
  "title": "On the arithmetic and geometric means of the prime numbers",
  "authors": [
    "Christian Axler"
  ],
  "comment": "18 pages, comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we establish explicit upper and lower bounds for the ratio of the arithmetic and geometric means of the prime numbers, which improve the current best estimates. Further, we prove several conjectures related to this ration stated by Hassani. In order to do this, we use explicit estimates for the prime counting function, Chebyshev's $\\vartheta$-function and the sum of the first $n$ prime numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-26T11:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L20",
      "11N37",
      "11A41"
    ],
    "keywords": [
      "prime numbers",
      "geometric means",
      "arithmetic",
      "current best estimates",
      "establish explicit upper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}