{
  "id": "1210.1818",
  "version": "v1",
  "published": "2012-10-05T17:28:18.000Z",
  "updated": "2012-10-05T17:28:18.000Z",
  "title": "Polylogarithms and multiple zeta values from free Rota-Baxter algebras",
  "authors": [
    "Li Guo",
    "Bin Zhang"
  ],
  "comment": "23 pages",
  "journal": "Science in China 53 (2010) 2239-2258",
  "categories": [
    "math.NT",
    "math.AC",
    "math.RA"
  ],
  "abstract": "We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara, Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator. We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series. We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-05T17:28:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M32",
      "16W99",
      "16W30"
    ],
    "keywords": [
      "multiple zeta values",
      "free rota-baxter algebras",
      "shuffle relations",
      "polylogarithms",
      "regularized mzvs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11425-010-4044-1",
      "journal": "Science in China A: Mathematics",
      "year": 2010,
      "month": "Jul",
      "volume": 53,
      "number": 9,
      "pages": 2239
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010ScChA..53.2239G"
    }
  }
}