{
  "id": "2002.11417",
  "version": "v1",
  "published": "2020-02-26T11:39:57.000Z",
  "updated": "2020-02-26T11:39:57.000Z",
  "title": "Two arithmetic applications of perturbations of composition operators",
  "authors": [
    "Sandro Bettin",
    "Sary Drappeau"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We estimate the spectral radius of perturbations of a particular family of composition operators, in a setting where the usual choices of norms do not account for the typical size of the perturbation. We apply this to estimate the growth rate of large moments of a Thue-Morse generating function and of the Stern sequence. This answers in particular a question of Mauduit, Montgomery and Rivat (2018).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-26T11:39:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A55",
      "11B85"
    ],
    "keywords": [
      "composition operators",
      "arithmetic applications",
      "perturbation",
      "usual choices",
      "thue-morse generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}