{
  "id": "math/0611849",
  "version": "v4",
  "published": "2006-11-28T03:20:39.000Z",
  "updated": "2014-09-29T16:42:44.000Z",
  "title": "Multiple Zeta Values and Ideles",
  "authors": [
    "Ivan Horozov"
  ],
  "comment": "This paper is a substantially revised version of the preprint \"Multiple Zeta Functions, Modular Forms and Adeles\" from 2006; better arranged comated to the previous version; 10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a shuffle relation. Thus, we recover in a unified way the two types of shuffle relations of multiple zeta values via the iterated integrals over finite ideles and via iterated integrals over the idele class group.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-11-30T16:47:51.000Z",
      "abstract": "In this paper we give two adelic interpretations of the multiple zeta values - one using iterated integrals over adeles and the other using iterated integrals over the finite adeles. Each of the interpretations leads to a shuffle relation. Thus, we recover the two types of shuffle relations of multiple zeta values via the adelic and the finite adelic iterated integrals. As an application of such integrals over the adeles we construct a function whose exponent is related to explicit formulas of the Hilbert symbol.",
      "comment": "This paper is a substantially revised version of the preprint \"Multiple Zeta Functions, Modular Forms and Adeles\" from 2006; 10 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-29T16:42:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M99",
      "11F11"
    ],
    "keywords": [
      "multiple zeta values",
      "shuffle relation",
      "finite adelic iterated integrals",
      "adelic interpretations",
      "finite adeles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11849H"
    }
  }
}