{
  "id": "1412.3505",
  "version": "v1",
  "published": "2014-12-11T00:27:03.000Z",
  "updated": "2014-12-11T00:27:03.000Z",
  "title": "Function Fields of Class Number One",
  "authors": [
    "Qibin Shen",
    "Shuhui Shi"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1975, [LMQ] listed 7 function felds over fnite felds (up to isomorphism) with positive genus and class number (i.e., the size of the divisor class group of degree zero) one and claimed to prove that these were the only ones such. In [S1], Claude Strirpe found 8th one! In this paper, we fix the argument in [LMQ] to show that this 8th example could have been found by [LMQ] method and is the only one, so that the list is now complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-11T00:27:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "class number",
      "function fields",
      "divisor class group",
      "fnite felds",
      "8th example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3505S"
    }
  }
}