{
  "id": "2209.05006",
  "version": "v1",
  "published": "2022-09-12T03:41:54.000Z",
  "updated": "2022-09-12T03:41:54.000Z",
  "title": "Higher genus polylogarithms on families of algebraic curves",
  "authors": [
    "Takashi Ichikawa"
  ],
  "comment": "15 pages, Sections 2 and 3 modify Sections 2 and 3 of arXiv:2010.11517. arXiv admin note: substantial text overlap with arXiv:2208.07013",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We describe polylogarithms on families of pointed curves of any genus using the theory of the universal Mumford curve which is the family of all pointed Mumford curves. As an application of the result, we show that the polylogarithms are expressed by rational polylogarithms and multiple zeta values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-12T03:41:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11G55",
      "11M32",
      "14H10",
      "14H15",
      "14D15",
      "32G20"
    ],
    "keywords": [
      "higher genus polylogarithms",
      "algebraic curves",
      "universal mumford curve",
      "multiple zeta values",
      "pointed mumford curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}