{
  "id": "1809.03444",
  "version": "v1",
  "published": "2018-09-10T16:32:48.000Z",
  "updated": "2018-09-10T16:32:48.000Z",
  "title": "Voronin Universality in several complex variables",
  "authors": [
    "Johan Andersson"
  ],
  "comment": "v1: 100 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove the Voronin universality theorem for the multiple Hurwitz zeta-function with rational or transcendental parameters in $\\mathbb{C}^n$ answering a question of Matsumoto. In particular this implies that the Euler-Zagier multiple zeta-function is universal in several complex variables and gives the first example of a Dirichlet series that is universal in more than one variable. We also prove joint and discrete universality results in several complex variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T16:32:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M32"
    ],
    "keywords": [
      "complex variables",
      "voronin universality theorem",
      "multiple hurwitz zeta-function",
      "euler-zagier multiple zeta-function",
      "discrete universality results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 100,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}