{
  "id": "1701.07546",
  "version": "v1",
  "published": "2017-01-26T02:05:34.000Z",
  "updated": "2017-01-26T02:05:34.000Z",
  "title": "Explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and applications",
  "authors": [
    "Takehiro Hasegawa"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Rank-2 Drinfeld modules are a function-field analogue of the elliptic curves, and the purpose of this paper is to investigate similarities and differences between rank-2 Drinfeld modules and elliptic curves in terms of supersingularity. Specifically, we provide an explicit formula for a supersingular polynomial for rank-2 Drinfeld modules and prove several basic properties. As an application, we give a numerical example of an asymptotically optimal tower of Drinfeld modular curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-26T02:05:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G09",
      "11R58"
    ],
    "keywords": [
      "drinfeld modules",
      "explicit formula",
      "supersingular polynomial",
      "application",
      "elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}