{
  "id": "1012.0675",
  "version": "v2",
  "published": "2010-12-03T09:34:15.000Z",
  "updated": "2013-09-10T20:13:19.000Z",
  "title": "Multiplicative zero-one laws and metric number theory",
  "authors": [
    "Victor Beresnevich",
    "Alan Haynes",
    "Sanju Velani"
  ],
  "comment": "13 pages",
  "journal": "Acta Arithmetica, 160(2), 101-114, 2013",
  "categories": [
    "math.NT"
  ],
  "abstract": "We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete `multiplicative' zero-one law is established akin to the `simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile `cross fibering principle'. In a nutshell it enables us to `lift' zero-one laws to higher dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-10T20:13:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric number theory",
      "multiplicative zero-one laws",
      "diophantine approximation",
      "duffin-schaeffer theorem",
      "cross fibering principle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.0675B"
    }
  }
}