{
  "id": "1307.3725",
  "version": "v1",
  "published": "2013-07-14T11:16:18.000Z",
  "updated": "2013-07-14T11:16:18.000Z",
  "title": "Algebraic independence of the Carlitz period and the positive characteristic multizeta values at n and (n,n)",
  "authors": [
    "Yoshinori Mishiba"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be the rational function field over the finite field of $q$ elements and $\\bar{k}$ its fixed algebraic closure. In this paper, we study algebraic relations over $\\bar{k}$ among the fundamental period $\\widetilde{\\pi}$ of the Carlitz module and the positive characteristic multizeta values $\\zeta(n)$ and $\\zeta(n,n)$ for an \"odd\" integer $n$, where we say that $n$ is \"odd\" if $q-1$ does not divide $n$. We prove that either they are algebraically independent over $\\bar{k}$ or satisfy some simple relation over $k$. We also prove that if $2n$ is \"odd\" then they are algebraically independent over $\\bar{k}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-14T11:16:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J93",
      "11M38",
      "11G09"
    ],
    "keywords": [
      "positive characteristic multizeta values",
      "algebraic independence",
      "carlitz period",
      "rational function field",
      "algebraically independent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3725M"
    }
  }
}