{
  "id": "1311.0754",
  "version": "v4",
  "published": "2013-11-04T16:25:34.000Z",
  "updated": "2014-07-18T07:17:37.000Z",
  "title": "Mertens' theorem and prime number theorem for Selberg class",
  "authors": [
    "Yoshikatsu Yashiro"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1874, Mertens proved the approximate formula for partial Euler product for Riemann zeta function at $s=1$, which is called Mertens' theorem. In this paper, we generalize Mertens' theorem for Selberg class and show the prime number theorem for Selberg class.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-07-18T07:17:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "11N05"
    ],
    "keywords": [
      "prime number theorem",
      "selberg class",
      "partial euler product",
      "riemann zeta function",
      "approximate formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0754Y"
    }
  }
}