{
  "id": "math/0302085",
  "version": "v2",
  "published": "2003-02-08T02:09:37.000Z",
  "updated": "2005-02-01T01:09:24.000Z",
  "title": "L-functions of Exponential sums over one-dimensional affinoid: Newton over Hodge",
  "authors": [
    "Hui June Zhu"
  ],
  "comment": "17 pages, LaTEX",
  "journal": "Inter. Math. Research Notices, 2004, no. 30, (2004), 1529--1550",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let p be a prime and let F_pbar be the algebraic closure of the finite field of p elements. Let f(x) be any one variable rational function over F_pbar with n poles of orders d_1, ...,d_n. Suppose p is coprime to d_i for every i. We prove that there exists a Hodge polygon, depending only on d_i's, which is a lower bound to the Newton polygon of L functions of exponential sums of f(x). Moreover, we show that these two polygons coincide if p=1 mod d_i for every i=1,...,n. As a corollary, we obtain a tight lower bound of Newton polygon of Artin-Schreier curve.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-01T01:09:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential sums",
      "one-dimensional affinoid",
      "l-functions",
      "newton polygon",
      "tight lower bound"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2085Z"
    }
  }
}