{
  "id": "1402.6758",
  "version": "v2",
  "published": "2014-02-27T01:12:41.000Z",
  "updated": "2014-09-10T13:21:25.000Z",
  "title": "Counting points on curves using a map to P^1",
  "authors": [
    "Jan Tuitman"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to the projective line. We develop all the necessary bounds, analyse the complexity of the algorithm and provide some examples computed with our implementation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-27T01:12:41.000Z",
      "title": "Counting points on curves using a map to $\\mathbf{P}^1$",
      "abstract": "We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to the projective line. We develop all the necessary bounds and analyse the complexity of the algorithm.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-10T13:21:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "counting points",
      "method extends kedlayas algorithm",
      "finite field",
      "necessary bounds",
      "zeta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6758T"
    }
  }
}