{
  "id": "2103.14307",
  "version": "v1",
  "published": "2021-03-26T07:45:15.000Z",
  "updated": "2021-03-26T07:45:15.000Z",
  "title": "On the asymptotic behavior of Sudler products along subsequences",
  "authors": [
    "Mario Neumüller"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\alpha \\in (0,1)$ and irrational. We investigate the asymptotic behaviour of sequences of certain trigonometric products (Sudler products) $(P_N(\\alpha))_{N\\in\\mathbb{N}}$ with $$P_N(\\alpha) =\\prod_{r=1}^N|2\\sin(\\pi r \\alpha)|.$$ More precisely, we are interested in the asymptotic behaviour of subsequences of the form $(P_{q_n(\\alpha)}(\\alpha))_{n\\in\\mathbb{N}}$, where $q_n(\\alpha)$ is the $n$th best approximation denominator of $\\alpha$. Interesting upper and lower bounds for the growth of these subsequences are given, and convergence results, obtained by Mestel and Verschueren (see arXiv:1411.2252math[DS]) and Grepstad and Neum\\\"uller (see arXiv:1801.09416[math.NT]), are generalized to the case of irrationals with bounded continued fraction coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-26T07:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D05",
      "41A60",
      "11J70",
      "11L15",
      "11K31"
    ],
    "keywords": [
      "sudler products",
      "asymptotic behavior",
      "subsequences",
      "asymptotic behaviour",
      "th best approximation denominator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}