{
  "id": "math/0609799",
  "version": "v2",
  "published": "2006-09-28T12:28:55.000Z",
  "updated": "2007-11-23T17:54:17.000Z",
  "title": "Multiple series connected to Hoffman's conjecture on multiple zeta values",
  "authors": [
    "Stéphane Fischler"
  ],
  "comment": "26 pages; small modifications",
  "journal": "Journal of Algebra 320 (2008), 1682-1703",
  "categories": [
    "math.NT"
  ],
  "abstract": "Recent results of Zlobin and Cresson-Fischler-Rivoal allow one to decompose any suitable $p$-uple series of hypergeometric type into a linear combination (over the rationals) of multiple zeta values of depth at most $p$; in some cases, only the multiple zeta values with 2's and 3's are involved (as in Hoffman's conjecture). In this text, we study the depth $p$ part of this linear combination, namely the contribution of the multiple zeta values of depth exactly $p$. We prove that it satisfies some symmetry property as soon as the $p$-uple series does, and make some conjectures on the depth $p-1$ part of the linear combination when $p=3$. Our result generalizes the property that (very) well-poised univariate hypergeometric series involve only zeta values of a given parity, which is crucial in the proof by Rivoal and Ball-Rivoal that $\\zeta(2n+1)$ is irrational for infinitely many $n \\geq 1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-23T17:54:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C20",
      "33C70",
      "11M06",
      "11J20",
      "11J72"
    ],
    "keywords": [
      "multiple zeta values",
      "multiple series",
      "hoffmans conjecture",
      "linear combination",
      "uple series"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9799F"
    }
  }
}