{
  "id": "1808.06782",
  "version": "v1",
  "published": "2018-08-21T06:51:08.000Z",
  "updated": "2018-08-21T06:51:08.000Z",
  "title": "The divisibility of zeta functions of cyclotomic function fields",
  "authors": [
    "Daisuke Shiomi"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we generalize Bernoulli-Goss polynomials, and give a criterion on the divisibility of zeta functions of cyclotomic function fields. As an application of our criterion, for a given polynomial $f(u)$, we prove that there are infinitely many cyclotomic function fields whose zeta polynomial is divided by $f(u)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-21T06:51:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclotomic function fields",
      "zeta functions",
      "divisibility",
      "zeta polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}