{
  "id": "2311.14937",
  "version": "v1",
  "published": "2023-11-25T05:53:50.000Z",
  "updated": "2023-11-25T05:53:50.000Z",
  "title": "Trigonometric polynomials with frequencies in the set of cubes",
  "authors": [
    "Mikhail R. Gabdullin",
    "Sergei V. Konyagin"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We prove that for any $\\epsilon>0$ and any trigonometric polynomial $f$ with frequencies in the set $\\{n^3: N \\leq n\\leq N+N^{2/3-\\epsilon}\\}$, one has $$ \\|f\\|_4 \\ll \\epsilon^{-1/4}\\|f\\|_2 $$ with implied constant being absolute. We also show that the set $\\{n^3: N\\leq n\\leq N+(0.5N)^{1/2}\\}$ is a Sidon set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-25T05:53:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "trigonometric polynomial",
      "frequencies",
      "sidon set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}