{
  "id": "math/0507121",
  "version": "v1",
  "published": "2005-07-06T14:29:02.000Z",
  "updated": "2005-07-06T14:29:02.000Z",
  "title": "On the poles of topological zeta functions",
  "authors": [
    "Ann Lemahieu",
    "Dirk Segers",
    "Willem Veys"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the topological zeta function Z_{top,f}(s) associated to a polynomial f with complex coefficients. This is a rational function in one variable and we want to determine the numbers that can occur as a pole of some topological zeta function; by definition these poles are negative rational numbers. We deal with this question in any dimension. Denote P_n := {s_0 | \\exists f in C[x_1,..., x_n] : Z_{top,f}(s) has a pole in s_0}. We show that {-(n-1)/2-1/i | i in Z_{>1}} is a subset of P_n; for n=2 and n=3, the last two authors proved before that these are exactly the poles less then -(n-1)/2. As main result we prove that each rational number in the interval [-(n-1)/2,0) is contained in P_n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-06T14:29:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological zeta function",
      "rational function",
      "negative rational numbers",
      "complex coefficients",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7121L"
    }
  }
}