{
  "id": "1805.11072",
  "version": "v1",
  "published": "2018-05-28T17:30:57.000Z",
  "updated": "2018-05-28T17:30:57.000Z",
  "title": "On certain mean values of logarithmic derivatives of $L$-functions and the related density functions",
  "authors": [
    "Masahiro Mine"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider some \"density function\" related to the value-distribution of $L$-functions. The first example of such a density function was given by Bohr and Jessen in 1930s, who studied the case of the Riemann zeta-function. The main subject of this paper is the construction of the density function for functions in a class of $L$-functions. We prove that certain mean values of $L$-functions in the class are represented as integrals involving the related density functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-28T17:30:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "11R42"
    ],
    "keywords": [
      "related density functions",
      "mean values",
      "logarithmic derivatives",
      "first example",
      "riemann zeta-function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}