{
  "id": "1801.03807",
  "version": "v1",
  "published": "2018-01-11T15:11:44.000Z",
  "updated": "2018-01-11T15:11:44.000Z",
  "title": "Iterated integrals on $\\mathbb{P}^{1}\\setminus\\{0,1,\\infty,z\\}$ and a class of relations among multiple zeta values",
  "authors": [
    "Minoru Hirose",
    "Nobuo Sato"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider iterated integrals on $\\mathbb{P}^{1}\\setminus\\{0,1,\\infty,z\\}$ and define a class of $\\mathbb{Q}$-linear relations among them, which arises from the differential structure of the iterated integrals with respect to $z$. We then define a new class of $\\mathbb{Q}$-linear relations among the multiple zeta values by taking their limits of $z\\rightarrow1$, which we call \\emph{confluence relations} (i.e., the relations obtained by the confluence of two punctured points). One of the significance of the confluence relations is that it gives a rich family and seems to exhaust all the linear relations among the multiple zeta values. As a good reason for this, we show that confluence relations imply both the regularized double shuffle relations and the duality relations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-11T15:11:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M32",
      "33E20"
    ],
    "keywords": [
      "multiple zeta values",
      "iterated integrals",
      "linear relations",
      "confluence relations",
      "regularized double shuffle relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}