{
  "id": "1909.00980",
  "version": "v1",
  "published": "2019-09-03T07:17:13.000Z",
  "updated": "2019-09-03T07:17:13.000Z",
  "title": "On the asymptotic behaviour of the sine product $\\prod_{r=1}^n|2\\sin(π r α)|$",
  "authors": [
    "Sigrid Grepstad",
    "Lisa Kaltenböck",
    "Mario Neumüller"
  ],
  "comment": "To appear in: D. Bilyk, J. Dick, F. Pillichshammer (Eds.) Discrepancy theory, Radon Series on Computational and Applied Mathematics",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we review recently established results on the asymptotic behaviour of the trigonometric product $P_n(\\alpha) = \\prod_{r=1}^n |2\\sin \\pi r \\alpha|$ as $n\\to \\infty$. We focus on irrationals $\\alpha$ whose continued fraction coefficients are bounded. Our main goal is to illustrate that when discussing the regularity of $P_n(\\alpha)$, not only the boundedness of the coefficients plays a role; also their size, as well as the structure of the continued fraction expansion of $\\alpha$, is important.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-03T07:17:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D05",
      "41A60",
      "11B39",
      "11L15",
      "11K31"
    ],
    "keywords": [
      "asymptotic behaviour",
      "sine product",
      "continued fraction expansion",
      "coefficients plays",
      "main goal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}