{
  "id": "1702.06938",
  "version": "v1",
  "published": "2017-02-22T18:51:25.000Z",
  "updated": "2017-02-22T18:51:25.000Z",
  "title": "Local Zeta Functions for Rational Functions and Newton Polyhedra",
  "authors": [
    "Miriam Bocardo-Gaspar",
    "W. A. Zúñiga-Galindo"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article, we introduce a notion of non-degeneracy, with respect to certain Newton polyhedra, for rational functions over non-Archimedean locals fields of arbitrary characteristic. We study the local zeta functions attached to non-degenerate rational functions, we show the existence of a meromorphic continuation for these zeta functions, as rational functions of $q^{-s}$, and give explicit formulas. In contrast with the classical local zeta functions, the meromorphic continuation of zeta functions for rational functions have poles with positive and negative real parts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-22T18:51:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G10",
      "11S40",
      "14M25"
    ],
    "keywords": [
      "newton polyhedra",
      "meromorphic continuation",
      "non-archimedean locals fields",
      "non-degenerate rational functions",
      "classical local zeta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}