{
  "id": "2404.16427",
  "version": "v1",
  "published": "2024-04-25T08:58:30.000Z",
  "updated": "2024-04-25T08:58:30.000Z",
  "title": "On algebraic independence of Taylor coefficients of certain Anderson-Thakur series",
  "authors": [
    "Daichi Matsuzuki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study algebraic independence problem for the Taylor coefficients of the Anderson-Thakur series arisen as deformation series of positive characteristic multiple zeta values (abbreviated as MZV's). These Taylor coefficients are simply specialization of hyperderivatives of the Anderson-Thakur series. We consider the prolongation of t-motives associated with MZV's, and then determine the dimension of the t-motivic Galois groups in question under certain hypothesis. By using Papanikolas' theory, it enables us to obtain the desired algebraic independence result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-25T08:58:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "taylor coefficients",
      "study algebraic independence problem",
      "positive characteristic multiple zeta values",
      "anderson-thakur series arisen",
      "t-motivic galois groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}