{
  "id": "2307.14992",
  "version": "v1",
  "published": "2023-07-27T16:39:57.000Z",
  "updated": "2023-07-27T16:39:57.000Z",
  "title": "Linear relations among algebraic points on tensor powers of the Carlitz module",
  "authors": [
    "Yen-Tsung Chen",
    "Ryotaro Harada"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In the present paper, we study linear equations on tensor powers of the Carlitz module using the theory of Anderson dual $t$-motives and a detailed analysis of a specific Frobenius difference equation. As an application, we derive some explicit sufficient conditions for the linear independence for Carlitz polylogarithms at algebraic points in both $\\infty$-adic and $v$-adic settings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-27T16:39:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J93",
      "33E50"
    ],
    "keywords": [
      "algebraic points",
      "carlitz module",
      "tensor powers",
      "linear relations",
      "specific frobenius difference equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}