{
  "id": "0803.4462",
  "version": "v4",
  "published": "2008-03-31T14:53:17.000Z",
  "updated": "2010-11-28T21:05:11.000Z",
  "title": "Hyperelliptic curves, L-polynomials, and random matrices",
  "authors": [
    "Kiran S. Kedlaya",
    "Andrew V. Sutherland"
  ],
  "comment": "Fixed 3 minor typos on pages 31 and 32, including a correction to Table 12. 44 pages",
  "journal": "Arithmetic, Geometry, Cryptography and Coding Theory (AGCT-11, 2007), Contemporary Mathematics volume 487, pp. 119-162, AMS, 2009",
  "doi": "10.1090/conm/487",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We analyze the distribution of unitarized L-polynomials Lp(T) (as p varies) obtained from a hyperelliptic curve of genus g <= 3 defined over Q. In the generic case, we find experimental agreement with a predicted correspondence (based on the Katz-Sarnak random matrix model) between the distributions of Lp(T) and of characteristic polynomials of random matrices in the compact Lie group USp(2g). We then formulate an analogue of the Sato-Tate conjecture for curves of genus 2, in which the generic distribution is augmented by 22 exceptional distributions, each corresponding to a compact subgroup of USp(4). In every case, we exhibit a curve closely matching the proposed distribution, and can find no curves unaccounted for by our classification.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-11-28T21:05:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M38",
      "11G20",
      "14G10",
      "15A52",
      "05E15"
    ],
    "keywords": [
      "random matrices",
      "hyperelliptic curve",
      "l-polynomials",
      "compact lie group usp",
      "katz-sarnak random matrix model"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.4462K"
    }
  }
}