{
  "id": "1512.04482",
  "version": "v1",
  "published": "2015-12-14T19:38:11.000Z",
  "updated": "2015-12-14T19:38:11.000Z",
  "title": "The parity theorem for multiple polylogarithms",
  "authors": [
    "Erik Panzer"
  ],
  "comment": "17 pages, supplemented by a list functional equations and a Maple program",
  "categories": [
    "math.NT"
  ],
  "abstract": "We generalize the well-known parity theorem for multiple zeta values (MZV) to functional equations of multiple polylogarithms (MPL). This reproves the parity theorem for MZV with an additional integrality statement, and also provides parity theorems for special values of MPL at roots of unity (also known as coloured MZV). We give explicit formulas in depths 2 and 3 and provide a computer program to compute the functional equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-14T19:38:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple polylogarithms",
      "functional equations",
      "multiple zeta values",
      "additional integrality statement",
      "well-known parity theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204482P"
    }
  }
}