{
  "id": "1111.5403",
  "version": "v2",
  "published": "2011-11-23T05:15:13.000Z",
  "updated": "2012-06-15T22:25:41.000Z",
  "title": "On the divisors of x^n-1 in F_p[x]",
  "authors": [
    "Lola Thompson"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In a recent paper, we considered integers n for which the polynomial x^n - 1 has a divisor in Z[x] of every degree up to n, and we gave upper and lower bounds for their distribution. In this paper, we consider those n for which the polynomial x^n-1 has a divisor in F_p[x] of every degree up to n, where p is a rational prime. Assuming the validity of the Generalized Riemann Hypothesis, we show that such integers n have asymptotic density 0.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-15T22:25:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bounds",
      "gave upper",
      "polynomial",
      "rational prime",
      "generalized riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5403T"
    }
  }
}