{
  "id": "math/0409372",
  "version": "v2",
  "published": "2004-09-20T23:59:34.000Z",
  "updated": "2004-12-04T23:04:29.000Z",
  "title": "L-Functions for Symmetric Products of Kloosterman Sums",
  "authors": [
    "Lei Fu",
    "Daqing Wan"
  ],
  "comment": "25 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and $\\infty$. We study the local monodromy of this representation at $\\infty$ using $l$-adic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of the $L$-functions of the symmetric products of the above representation. Our results generalize some results of Robba obtained through $p$-adic method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-12-04T23:04:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "14F20"
    ],
    "keywords": [
      "symmetric products",
      "l-functions",
      "adic method",
      "function field unramfied outside",
      "classical kloosterman sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9372F"
    }
  }
}