{
  "id": "2002.10554",
  "version": "v1",
  "published": "2020-02-24T21:34:59.000Z",
  "updated": "2020-02-24T21:34:59.000Z",
  "title": "Irreducibility of random polynomials of bounded degree",
  "authors": [
    "Huy Tuan Pham",
    "Max Wenqiang Xu"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "It is known that random monic integral polynomials of bounded degree $d$ and integral coefficients distributed uniformly and independently in $[-H,H]$ are irreducible over $\\mathbb{Z}$ with probability tending to $1$ as $H\\to \\infty$. In this paper, we prove that the same conclusion holds under much more general distributions of the coefficients, allowing them to be dependently and nonuniformly distributed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-24T21:34:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded degree",
      "random polynomials",
      "irreducibility",
      "random monic integral polynomials",
      "general distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}