{
  "id": "1209.2398",
  "version": "v2",
  "published": "2012-09-11T19:08:10.000Z",
  "updated": "2012-11-06T00:12:36.000Z",
  "title": "Lower Bounds for $L_1$ Discrepancy",
  "authors": [
    "Armen Vagharshakyan"
  ],
  "comment": "a slightly different version of the article is accepted to \"Mathematika\"",
  "doi": "10.1112/S0025579312001180",
  "categories": [
    "math.CA",
    "math.NT",
    "math.PR"
  ],
  "abstract": "We find the best asymptotic lower bounds for the coefficient of the leading term of the $L_1$ norm of the two-dimensional (axis-parallel) discrepancy that can be obtained by K.Roth's orthogonal function method among a large class of test functions. We use methods of combinatorics, probability, complex and harmonic analysis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-06T00:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38"
    ],
    "keywords": [
      "discrepancy",
      "roths orthogonal function method",
      "best asymptotic lower bounds",
      "harmonic analysis",
      "test functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2398V"
    }
  }
}