{
  "id": "2412.07908",
  "version": "v2",
  "published": "2024-12-10T20:33:45.000Z",
  "updated": "2024-12-17T22:18:33.000Z",
  "title": "Transcendence of Hecke-Mahler Series",
  "authors": [
    "Florian Luca",
    "Joel Ouaknine",
    "James Worrell"
  ],
  "categories": [
    "math.NT",
    "cs.FL"
  ],
  "abstract": "We prove transcendence of the Hecke-Mahler series $\\sum_{n=0}^\\infty f(\\lfloor n\\theta+\\alpha \\rfloor) \\beta^{-n}$, where $f(x) \\in \\mathbb{Z}[x]$ is a non-constant polynomial $\\alpha$ is a real number, $\\theta$ is an irrational real number, and $\\beta$ is an algebraic number such that $|\\beta|>1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-12-17T22:18:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J87"
    ],
    "keywords": [
      "hecke-mahler series",
      "transcendence",
      "irrational real number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}