{
  "id": "0903.1238",
  "version": "v3",
  "published": "2009-03-06T16:04:06.000Z",
  "updated": "2009-08-28T20:39:07.000Z",
  "title": "Motivic Zeta Functions for Curve Singularities",
  "authors": [
    "J. J. Moyano-Fernandez",
    "W. A. Zuniga-Galindo"
  ],
  "comment": "Several typos and small errors were corrected. The definition of universal zeta function was modified",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring O_{P,X} at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if O_{P,X} is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincare series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincare series introduced by Campillo, Delgado and Gusein-Zade.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-28T20:39:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H20",
      "14G10",
      "32S40",
      "11S40"
    ],
    "keywords": [
      "motivic zeta functions",
      "curve singularities",
      "universal zeta function specializes",
      "algebraic curve",
      "rational singular point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1238M"
    }
  }
}