{
  "id": "2008.05253",
  "version": "v1",
  "published": "2020-08-12T11:59:50.000Z",
  "updated": "2020-08-12T11:59:50.000Z",
  "title": "On the number of point of given order on odd degree hyperelliptic curves",
  "authors": [
    "John Boxall"
  ],
  "comment": "All comments welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For integers $N\\geq 3$ and $g\\geq 1$, we study bounds on the cardinality of the set of points of order dividing $N$ lying on a hyperelliptic curve of genus $g$ embedded in its jacobian using a Weierstrass point as base point. This leads us to revisit division polynomials introduced by Cantor in 1995 and strengthen a divisibility result proved by him. Several examples are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-12T11:59:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "11G20"
    ],
    "keywords": [
      "odd degree hyperelliptic curves",
      "revisit division polynomials",
      "study bounds",
      "weierstrass point",
      "base point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}