{
  "id": "1011.0195",
  "version": "v1",
  "published": "2010-10-31T19:19:12.000Z",
  "updated": "2010-10-31T19:19:12.000Z",
  "title": "Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory",
  "authors": [
    "Djurdje Cvijović"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Borwein and Broadhurst, using experimental-mathematics techniques, in 1998 identified numerous hyperbolic 3-manifolds whose volumes are rationally related to values of various Dirichlet L series $\\textup{L}_{d}(s)$. In particular, in the simplest case of an ideal tetrahedron in hyperbolic space, they conjectured that a dilogarithmic integral representing the volume equals to $\\textup{L}_{-7}(2)$. Here we have provided a formal proof of this conjecture which has been recently numerically verified (to at least 19,995 digits, using 45 minutes on 1024 processors) in cutting-edge computing experiments. The proof essentially relies on the results of Zagier on the formula for the value of Dedekind zeta function $\\zeta_{\\mathbb{K}}(2)$ for an arbitrary field $\\mathbb{K}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-31T19:19:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum field theory",
      "dilogarithmic integral arising",
      "borwein-broadhurst conjecture",
      "dedekind zeta function",
      "arbitrary field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0195C"
    }
  }
}