{
  "id": "math/0206217",
  "version": "v1",
  "published": "2002-06-20T20:19:09.000Z",
  "updated": "2002-06-20T20:19:09.000Z",
  "title": "Units, polyhedra, and a conjecture of Satake",
  "authors": [
    "Paul E. Gunnells",
    "Jacob Sturm"
  ],
  "comment": "plain tex, uses epsf",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $F/\\QQ $ be a totally real number field of degree $n$. We explicitly evaluate a certain sum of rational functions over a infinite fan of $F$-rational polyhedral cones in terms of the norm map $\\Norm \\colon F\\to \\QQ $. This completes Sczech's combinatorial proof of Satake's conjecture connecting the special values of $L$-series associated to cusp singularities with intersection numbers of divisors in their toroidal resolutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-06-20T20:19:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F41",
      "11R42",
      "14M25"
    ],
    "keywords": [
      "completes sczechs combinatorial proof",
      "totally real number field",
      "rational polyhedral cones",
      "rational functions",
      "infinite fan"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......6217G"
    }
  }
}