{
  "id": "2012.09840",
  "version": "v1",
  "published": "2020-12-17T18:57:18.000Z",
  "updated": "2020-12-17T18:57:18.000Z",
  "title": "Functional equations of polygonal type for multiple polylogarithms in weights 5, 6 and 7",
  "authors": [
    "Steven Charlton",
    "Herbert Gangl",
    "Danylo Radchenko"
  ],
  "comment": "6 pages, 4 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We present new functional equations in weights 5, 6 and 7 and use them for explicit depth reduction of multiple polylogarithms. These identities generalize the crucial identity $\\mathbf{Q}_4$ from the recent work of Goncharov and Rudenko that was used in their proof of the weight 4 case of Zagier's Polylogarithm Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-17T18:57:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G55",
      "33E20",
      "39B32"
    ],
    "keywords": [
      "multiple polylogarithms",
      "functional equations",
      "polygonal type",
      "zagiers polylogarithm conjecture",
      "explicit depth reduction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}