{
  "id": "1705.07865",
  "version": "v1",
  "published": "2017-05-22T17:15:27.000Z",
  "updated": "2017-05-22T17:15:27.000Z",
  "title": "On the value-distributions of logarithmic derivatives of Dedekind zeta functions",
  "authors": [
    "Masahiro Mine"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the distributions of values of logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main result is determining the density functions of such value-distributions for any algebraic number field. The Fourier transformations of the density functions have infinite product representations that come from the Euler products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-22T17:15:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dedekind zeta functions",
      "logarithmic derivatives",
      "value-distributions",
      "density functions",
      "algebraic number field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}