{
  "id": "1305.4016",
  "version": "v4",
  "published": "2013-05-17T08:54:57.000Z",
  "updated": "2014-09-19T07:53:45.000Z",
  "title": "A calculation of $L$-series in terms of Jacobi sums",
  "authors": [
    "Alvarez Arturo"
  ],
  "comment": "18 Pages, Added a new section",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let us consider a cyclic extension of a function field defined over a finite field. For a character (non-trivial) of this extension, we calculate, as a linear combinations of products of Jacobi sums, the coefficients of the polynomial given by its Dirichtlet $L$-series. In the last section we show applications of this calculation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-09T08:07:47.000Z",
      "abstract": "Let us consider a cyclic extension of a function field defined over a finite field. For a character (non-trivial) of this extension, we calculate, as a linear combinations of products of Jacobi sums, the coefficients of the polynomial given by its Dirichtlet $L$-series.",
      "comment": "13 Pages, Removed chapter 5",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-19T07:53:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14G10"
    ],
    "keywords": [
      "jacobi sums",
      "calculation",
      "linear combinations",
      "cyclic extension",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4016A"
    }
  }
}