{
  "id": "math/0501120",
  "version": "v1",
  "published": "2005-01-09T10:56:06.000Z",
  "updated": "2005-01-09T10:56:06.000Z",
  "title": "Primitive Roots in Quadratic Fields II",
  "authors": [
    "Joseph Cohen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper is continuation of the paper \"Primitive roots in quadratic field\". We consider an analogue of Artin's primitive root conjecture for algebraic numbers which is not a unit in real quadratic fields. Given such an algebraic number, for a rational prime $p$ which is inert in the field the maximal order of the unit modulo $p$ is $p^2-1$. An extension of Artin's conjecture is that there are infinitely many such inert primes for which this order is maximal. we show that for any choice of 85 algebraic numbers satisfying a certain simple restriction, there is at least one of the algebraic numbers which satisfies the above version of Artin's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-09T10:56:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11N69"
    ],
    "keywords": [
      "algebraic number",
      "artins conjecture",
      "artins primitive root conjecture",
      "real quadratic fields",
      "simple restriction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1120C"
    }
  }
}