{
  "id": "0710.5911",
  "version": "v2",
  "published": "2007-10-31T17:37:01.000Z",
  "updated": "2012-09-17T09:00:44.000Z",
  "title": "The motivic zeta function and its smallest poles",
  "authors": [
    "Dirk Segers",
    "Lise Van Proeyen",
    "Willem Veys"
  ],
  "journal": "Journal of Algebra 317 (2007) 851-866",
  "doi": "10.1016/j.jalgebra.2007.05.012",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let f be a regular function on a nonsingular complex algebraic variety of dimension d. We prove a formula for the motivic zeta function of f in terms of an embedded resolution. This formula is over the Grothendieck ring itself, and specializes to the formula of Denef and Loeser over a certain localization. We also show that the space of n-jets satisfying f=0 can be partitioned into locally closed subsets which are isomorphic to a cartesian product of some variety with an affine space of dimension the round up of dn/2. Finally, we look at the consequences for the poles of the motivic zeta function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-17T09:00:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14E15",
      "14J17"
    ],
    "keywords": [
      "motivic zeta function",
      "smallest poles",
      "nonsingular complex algebraic variety",
      "regular function",
      "cartesian product"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.5911S"
    }
  }
}