{
  "id": "2002.08120",
  "version": "v1",
  "published": "2020-02-19T11:42:24.000Z",
  "updated": "2020-02-19T11:42:24.000Z",
  "title": "On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial",
  "authors": [
    "Antonio J. Di Scala",
    "Carlo Sanna",
    "Edoardo Signorini"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently, Blanco-Chac\\'on proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by giving some upper bounds for the condition number $\\operatorname{Cond}(V_n)$ of the Vandermonde matrix $V_n$ associated to the $n$th cyclotomic polynomial. We prove some results on the singular values of $V_n$ and, in particular, we determine $\\operatorname{Cond}(V_n)$ for $n = 2^k p^\\ell$, where $k, \\ell \\geq 0$ are integers and $p$ is an odd prime number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-19T11:42:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C99",
      "15A12",
      "15B05"
    ],
    "keywords": [
      "nth cyclotomic polynomial",
      "condition number",
      "vandermonde matrix",
      "odd prime number",
      "cyclotomic number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}