{
  "id": "math/0312423",
  "version": "v2",
  "published": "2003-12-23T05:04:03.000Z",
  "updated": "2005-01-30T07:49:25.000Z",
  "title": "Zeta functions of totally ramified p-covers of the projective line",
  "authors": [
    "Hanfeng Li",
    "Hui June Zhu"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper we prove that there exists a Zariski dense open subset U defined over the rationals Q in the space of all one-variable rational functions with arbitrary k poles of prescribed orders, such that for every geometric point f in U(Qbar)$, the L-function of the exponential sum of f at a prime p has Newton polygon approaching the Hodge polygon as p approaches infinity. As an application to algebraic geometry, we prove that the p-adic Newton polygon of the zeta function of a p-cover of the projective line totally ramified at arbitrary k points of prescribed orders has an asymptotic generic lower bound.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-30T07:49:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zeta function",
      "totally ramified p-covers",
      "projective line",
      "zariski dense open subset",
      "asymptotic generic lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12423L"
    }
  }
}