{
  "id": "1610.08651",
  "version": "v1",
  "published": "2016-10-27T08:14:09.000Z",
  "updated": "2016-10-27T08:14:09.000Z",
  "title": "On holomorphic Artin L-functions",
  "authors": [
    "Florin Nicolae"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K/\\mathbb Q$ be a finite Galois extension, $s_0\\in \\mathbb C\\setminus \\{1\\}$, ${\\it Hol}(s_0)$ the semigroup of Artin L-functions holomorphic at $s_0$. If the Galois group is almost monomial then Artin's L-functions are holomorphic at $s_0$ if and only if $ {\\it Hol}(s_0)$ is factorial. This holds also if $s_0$ is a zero of an irreducible L-function of dimension $\\leq 2$, without any condition on the Galois group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-27T08:14:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42"
    ],
    "keywords": [
      "holomorphic artin l-functions",
      "galois group",
      "finite galois extension",
      "artin l-functions holomorphic",
      "artins l-functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}