{
  "id": "1707.04382",
  "version": "v1",
  "published": "2017-07-14T05:01:54.000Z",
  "updated": "2017-07-14T05:01:54.000Z",
  "title": "On the density function for the value-distribution of automorphic $L$-functions",
  "authors": [
    "Kohji Matsumoto",
    "Yumiko Umegaki"
  ],
  "comment": "21pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The Bohr-Jessen limit theorem is a probabilistic limit theorem on the value-distribution of the Riemann zeta-function in the critical strip. Moreover their limit measure can be written as an integral involving a certaindensity function. The existence of the limit measure is now known for a quite general class of zeta-functions, but the integral expression has been proved only for some special cases (such as Dedekind zeta-functions). In this paper we give an alternative proof of the existence of the limit measure for a general setting, and then prove the integral expression, with an explicitly constructed density function, for the case of automorphic L-functions attached to primitive forms with respect to congruence subgroups Gamma_0(N).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-14T05:01:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11M41"
    ],
    "keywords": [
      "limit measure",
      "value-distribution",
      "integral expression",
      "bohr-jessen limit theorem",
      "probabilistic limit theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}