{
  "id": "1208.2633",
  "version": "v1",
  "published": "2012-08-13T16:33:59.000Z",
  "updated": "2012-08-13T16:33:59.000Z",
  "title": "A Note on the Mean Value of $L$--functions in Function Fields",
  "authors": [
    "Julio Andrade"
  ],
  "comment": "Accepted for publication in International Journal of Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "An asymptotic formula for the sum $\\sum L(1,\\chi)$ is established for a family of hyperelliptic curves of genus $g$ over a fixed finite field $\\mathbb{F}_q$ as $g\\rightarrow\\infty$ making use of the analogue of the approximate functional equation for such $L$--functions. As a corollary, we obtain a formula for the average of the class number of the associated rings $\\mathbb{F}_{q}[T,sqrt{D}]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-13T16:33:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11R29",
      "14G10"
    ],
    "keywords": [
      "function fields",
      "mean value",
      "approximate functional equation",
      "class number",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2633A"
    }
  }
}