{
  "id": "2006.00549",
  "version": "v1",
  "published": "2020-05-31T15:58:22.000Z",
  "updated": "2020-05-31T15:58:22.000Z",
  "title": "On Proinov's lower bound for the diaphony",
  "authors": [
    "Nathan Kirk"
  ],
  "comment": "25 pages, 2 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1986, Proinov published an explicit lower bound for the diaphony of both finite and infinite sequences of points in the s dimensional unit cube. To the best of our knowledge, the proofs of these results were so far only available in a monograph of Proinov written in Bulgarian. The first contribution of our paper is to give a self contained version of Proinov's proof in English. Along the way, we improve the asymptotic constants using recent results of Hinrichs and Markhasin. Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-31T15:58:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "proinovs lower bound",
      "explicit lower bound",
      "infinite sequences",
      "dimensional unit cube",
      "proinov written"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}