{
  "id": "1703.08827",
  "version": "v1",
  "published": "2017-03-26T15:37:15.000Z",
  "updated": "2017-03-26T15:37:15.000Z",
  "title": "On Dirichlet series and functional equations",
  "authors": [
    "Alexey Kuznetsov"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "There exist many explicit evaluations of Dirichlet series. Most of them are constructed via the same approach: by taking products or powers of Dirichlet series with a known Euler product representation. In this paper we derive a result of a new flavour: we give the Dirichlet series representation to solutions of certain functional equations. Our result seems to be a Dirichlet series analogue of the well known Lagrange-Burmann formula for power series. The proof is probabilistic in nature and is based on Kendall's identity, which arises in the fluctuation theory of Levy processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-26T15:37:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41",
      "60G51"
    ],
    "keywords": [
      "functional equations",
      "euler product representation",
      "dirichlet series representation",
      "dirichlet series analogue",
      "explicit evaluations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}