{
  "id": "1804.06084",
  "version": "v1",
  "published": "2018-04-17T07:48:57.000Z",
  "updated": "2018-04-17T07:48:57.000Z",
  "title": "Central Limit Theorems for Diophantine approximants",
  "authors": [
    "Michael Björklund",
    "Alexander Gorodnik"
  ],
  "comment": "50 pages",
  "categories": [
    "math.DS",
    "math.NT",
    "math.PR"
  ],
  "abstract": "In this paper we study counting functions representing the number of solutions of systems of linear inequalities which arise in the theory of Diophantine approximation. We develop a method that allows us to explain the random-like behavior that these functions exhibit and prove a Central Limit Theorem for them. Our approach is based on a quantitative study of higher-order correlations for functions defined on the space of lattices and a novel technique for estimating cumulants of Siegel transforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T07:48:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "diophantine approximants",
      "siegel transforms",
      "diophantine approximation",
      "higher-order correlations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}