{
  "id": "1504.00508",
  "version": "v1",
  "published": "2015-04-02T10:59:01.000Z",
  "updated": "2015-04-02T10:59:01.000Z",
  "title": "The functional equation for L-functions of hyperelliptic curves",
  "authors": [
    "Michel Börner",
    "Irene I. Bouw",
    "Stefan Wewers"
  ],
  "comment": "27 pages, 4 figures",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We compute the $L$-functions of a large class of algebraic curves, and verify the expected functional equation numerically. Our computations are based on our previous results on stable reduction to calculate the local $L$-factor and the conductor exponent at the primes of bad reduction. Most of our examples are hyperelliptic curves of genus $g\\geq 2$ defined over $\\mathbb{Q}$ which have semistable reduction at every prime $p$. We also treat a few more general examples of superelliptic curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-02T10:59:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40",
      "14G10",
      "11G20"
    ],
    "keywords": [
      "hyperelliptic curves",
      "l-functions",
      "large class",
      "bad reduction",
      "algebraic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150400508B"
    }
  }
}