{
  "id": "2103.05836",
  "version": "v1",
  "published": "2021-03-10T02:43:04.000Z",
  "updated": "2021-03-10T02:43:04.000Z",
  "title": "Hyperderivatives of periods and quasi-periods for Anderson $t$-modules",
  "authors": [
    "Changningphaabi Namoijam",
    "Matthew A. Papanikolas"
  ],
  "comment": "111 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate periods, quasi-periods, logarithms, and quasi-logarithms of Anderson $t$-modules, as well as their hyperderivatives. We develop a comprehensive account of how these values can be obtained through rigid analytic trivializations of abelian and $\\mathbf{A}$-finite $t$-modules. To do this we build on the exponentiation theorem of Anderson and investigate quasi-periodic extensions of $t$-modules through Anderson generating functions. By applying these results to prolongation $t$-modules of Maurischat, we integrate hyperderivatives of these values together with previous work of Brownawell and Denis in this framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-10T02:43:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G09",
      "11J93",
      "33E50"
    ],
    "keywords": [
      "quasi-periods",
      "rigid analytic trivializations",
      "exponentiation theorem",
      "quasi-periodic extensions",
      "anderson generating functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 111,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}