{
  "id": "2212.10128",
  "version": "v1",
  "published": "2022-12-20T09:55:05.000Z",
  "updated": "2022-12-20T09:55:05.000Z",
  "title": "Sums of transcendental dilates",
  "authors": [
    "David Conlon",
    "Jeck Lim"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that there is an absolute constant $c>0$ such that $|A+\\lambda\\cdot A|\\geq e^{c\\sqrt{\\log |A|}}|A|$ for any finite subset $A$ of $\\mathbb{R}$ and any transcendental number $\\lambda\\in\\mathbb{R}$. By a construction of Konyagin and Laba, this is best possible up to the constant $c$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-20T09:55:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D99",
      "11B13",
      "11B75",
      "11B30"
    ],
    "keywords": [
      "transcendental dilates",
      "transcendental number",
      "absolute constant",
      "finite subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}