{
  "id": "1611.02582",
  "version": "v1",
  "published": "2016-11-08T16:06:06.000Z",
  "updated": "2016-11-08T16:06:06.000Z",
  "title": "A note on Picard curves of CM-type",
  "authors": [
    "Joan-C. Lario",
    "Anna Somoza"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend the list of Picard curves of CM-type given by Koike and Weng. In particular, our list includes defining equations for the complete list of Picard curves of CM-type defined over $\\mathbb{Q}$ up to isomorphism. To this end, we improve their algorithm in some aspects: one needs to precise a root of unity in an accurate application of a Thomae-like formula well-suited for the Picard case, and also use an optimized strategy to evaluate the Riemann theta-series involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-08T16:06:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "picard curves",
      "complete list",
      "accurate application",
      "picard case",
      "riemann theta-series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}