{
  "id": "1606.04137",
  "version": "v1",
  "published": "2016-06-13T21:04:36.000Z",
  "updated": "2016-06-13T21:04:36.000Z",
  "title": "Combinatorial proof of the transcendence of $L(1,χ_s)/Π$",
  "authors": [
    "Yining Hu"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We give a combinatorial proof of the transcendence of $L(1,\\chi_s)/\\Pi$, where $L(1,\\chi_s)$ (resp. $\\Pi$) is the analogue in characteristic $p$ of the function $L$ of Dirichlet (resp. $\\pi$). This result has been proven by G. Damamme using the criteria of de Mathan. Our proof is based on the Theorem of Christol and another property of $k$-automatic sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-13T21:04:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial proof",
      "transcendence",
      "automatic sequences",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}