{
  "id": "1611.08128",
  "version": "v1",
  "published": "2016-11-24T10:32:38.000Z",
  "updated": "2016-11-24T10:32:38.000Z",
  "title": "On the distribution of polynomials with bounded height",
  "authors": [
    "Csanád Bertók",
    "Lajos Hajdu",
    "Attila Pethő"
  ],
  "comment": "12 pages, 4 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "We provide an asymptotic expression for the probability that a randomly chosen polynomial with given degree, having integral coefficients bounded by some B, has a prescribed signature. We also give certain related formulas and numerical results along this line. Our theorems are closely related to earlier results of Akiyama and Peth\\H{o}, and also yield extensions of recent results of Dubickas and Sha.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-24T10:32:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08"
    ],
    "keywords": [
      "bounded height",
      "distribution",
      "randomly chosen polynomial",
      "integral coefficients",
      "asymptotic expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}