{
  "id": "1407.3099",
  "version": "v1",
  "published": "2014-07-11T10:33:10.000Z",
  "updated": "2014-07-11T10:33:10.000Z",
  "title": "Conjectures for the integral moments and ratios of L-functions over function fields",
  "authors": [
    "J. C. Andrade",
    "J. P. Keating"
  ],
  "comment": "40 pages",
  "journal": "Journal of Number Theory, Volume 142, September 2014, Pages 102-148",
  "doi": "10.1016/j.jnt.2014.02.019",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend to the function field setting the heuristic previously developed, by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments and ratios of $L$-functions defined over number fields. Specifically, we give a heuristic for the moments and ratios of a family of $L$-functions associated with hyperelliptic curves of genus $g$ over a fixed finite field $\\mathbb{F}_{q}$ in the limit as $g\\rightarrow\\infty$. Like in the number field case, there is a striking resemblance to the corresponding formulae for the characteristic polynomials of random matrices. As an application, we calculate the one-level density for the zeros of these $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-11T10:33:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11M50",
      "14G10"
    ],
    "keywords": [
      "integral moments",
      "function field",
      "l-functions",
      "conjectures",
      "number field case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.3099A"
    }
  }
}