{
  "id": "1906.00747",
  "version": "v1",
  "published": "2019-06-03T12:37:28.000Z",
  "updated": "2019-06-03T12:37:28.000Z",
  "title": "Quantitative non-divergence and Diophantine approximation on manifolds",
  "authors": [
    "Dmitry Kleinbock",
    "Victor Beresnevich"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "The goal of this survey is to discuss the Quantitative non-Divergence estimate on the space of lattices and present a selection of its applications. The topics covered include extremal manifolds, Khintchine-Groshev type theorems, rational points lying close to manifolds and badly approximable points on manifolds. The main emphasis is on the role of the Quantitative non-Divergence estimate in the aforementioned topics within the theory of Diophantine approximation, and therefore this paper should not be regarded as a comprehensive overview of the area.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T12:37:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17"
    ],
    "keywords": [
      "diophantine approximation",
      "quantitative non-divergence estimate",
      "khintchine-groshev type theorems",
      "rational points lying close",
      "main emphasis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}