{
  "id": "1609.05557",
  "version": "v1",
  "published": "2016-09-18T21:47:18.000Z",
  "updated": "2016-09-18T21:47:18.000Z",
  "title": "Multiple polylogarithms in weight 4",
  "authors": [
    "Herbert Gangl"
  ],
  "comment": "21 pages, link to home page with (long) Mathematica-readable expressions",
  "categories": [
    "math.NT",
    "math-ph",
    "math.KT",
    "math.MP"
  ],
  "abstract": "We clarify the relationship between different multiple polylogarithms in weight~4 by writing suitable linear combinations of a given type of iterated integral I_{n_1,...,n_d}(z_1,...,z_d), in depth d>1 and weight \\sum_i n_i=4 in terms of the classical tetralogarithm Li_4. In the process, we prove a statement conjectured by Goncharov which can be rephrased as writing the sum of iterated integrals I_{3,1}(V(x,y),z), where V(x,y) denotes a formal version of the five term relation for the dilogarithm, in terms of Li_4-terms (we need 122 such).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-18T21:47:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G55",
      "14F42",
      "33E20",
      "39B32"
    ],
    "keywords": [
      "multiple polylogarithms",
      "iterated integral",
      "formal version",
      "writing suitable linear combinations",
      "term relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}