{
  "id": "0804.0578",
  "version": "v1",
  "published": "2008-04-03T15:23:40.000Z",
  "updated": "2008-04-03T15:23:40.000Z",
  "title": "Characteristic polynomials of automorphisms of hyperelliptic curves",
  "authors": [
    "Robert M. Guralnick",
    "Everett W. Howe"
  ],
  "comment": "LaTeX, 11 pages",
  "journal": "pp. 101-112 in: Arithmetic, Geometry, Cryptography and Coding Theory (G. Lachaud, C. Ritzenthaler, and M. A. Tsfasman, eds.), Contemporary Mathematics 487, American Mathematical Society, Providence, RI, 2009",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let alpha be an automorphism of a hyperelliptic curve C of genus g, and let alpha' be the automorphism of P^1 induced by alpha. Let n be the order of alpha and let n' be the order of alpha'. We show that the triple (g,n,n') completely determines the characteristic polynomial of the automorphism alpha^* of the Jacobian of C, unless n is even, n=n', and (2g+2)/n is even, in which case there are two possibilities. We give explicit formulas for the characteristic polynomial in all cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-03T15:23:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H37",
      "14H40"
    ],
    "keywords": [
      "characteristic polynomial",
      "hyperelliptic curve",
      "automorphism",
      "explicit formulas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.0578G"
    }
  }
}