{
  "id": "0812.4994",
  "version": "v1",
  "published": "2008-12-30T00:44:23.000Z",
  "updated": "2008-12-30T00:44:23.000Z",
  "title": "Functional Equations of $L$-Functions for Symmetric Products of the Kloosterman Sheaf",
  "authors": [
    "Lei Fu",
    "Daqing Wan"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We determine the (arithmetic) local monodromy at 0 and at $\\infty$ of the Kloosterman sheaf using local Fourier transformations and Laumon's stationary phase principle. We then calculate $\\epsilon$-factors for symmetric products of the Kloosterman sheaf. Using Laumon's product formula, we get functional equations of $L$-functions for these symmetric products, and prove a conjecture of Evans on signs of constants of functional equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-30T00:44:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "14G15"
    ],
    "keywords": [
      "functional equations",
      "symmetric products",
      "kloosterman sheaf",
      "laumons stationary phase principle",
      "laumons product formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4994F"
    }
  }
}