{
  "id": "1710.08252",
  "version": "v1",
  "published": "2017-10-23T13:10:03.000Z",
  "updated": "2017-10-23T13:10:03.000Z",
  "title": "Prolongations of t-motives and algebraic independence of periods",
  "authors": [
    "Andreas Maurischat"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article we show that the coordinates of a period lattice generator of the $n$-th tensor power of the Carlitz module are algebraically independent, if $n$ is prime to the characteristic. The main part of the paper, however, is devoted to a general construction for $t$-motives which we call prolongation, and which gives the necessary background for our proof of the algebraic independence. Another incredient is a theorem which shows hypertranscendence for the Anderson-Thakur function $\\omega(t)$, i.e. that $\\omega(t)$ and all its hyperderivatives with respect to $t$ are algebraically independent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-23T13:10:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J93",
      "11G09",
      "13N99"
    ],
    "keywords": [
      "algebraic independence",
      "prolongation",
      "period lattice generator",
      "th tensor power",
      "algebraically independent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}