{
  "id": "1510.00536",
  "version": "v1",
  "published": "2015-10-02T09:19:59.000Z",
  "updated": "2015-10-02T09:19:59.000Z",
  "title": "Correlations between real conjugate algebraic numbers",
  "authors": [
    "Friedrich Götze",
    "Dzianis Kaliada",
    "Dmitry Zaporozhets"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT",
    "math.CA",
    "math.PR"
  ],
  "abstract": "For $B\\subset\\mathbb{R}^k$ denote by $\\Phi_k(Q;B)$ the number of ordered $k$-tuples in $B$ of real conjugate algebraic numbers of degree $\\leq n$ and naive height $\\leq Q$. We show that $$ \\Phi_k(Q;B) = \\frac{(2Q)^{n+1}}{2\\zeta(n+1)} \\int_{B} \\rho_k(\\mathbf{x})\\,d\\mathbf{x} + O\\left(Q^n\\right),\\quad Q\\to \\infty, $$ where the function $\\rho_k$ will be given explicitly. If $n=2$, then an additional factor $\\log Q$ appears in the reminder term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-02T09:19:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N45",
      "11C08",
      "60G55",
      "11R80"
    ],
    "keywords": [
      "real conjugate algebraic numbers",
      "correlations",
      "additional factor",
      "reminder term",
      "naive height"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000536G"
    }
  }
}