{
  "id": "1904.04457",
  "version": "v1",
  "published": "2019-04-09T04:03:45.000Z",
  "updated": "2019-04-09T04:03:45.000Z",
  "title": "Hausdorff dimension of the large values of Weyl sums",
  "authors": [
    "Changhao Chen",
    "Igor E. Shparlinski"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "The authors have recently obtained a lower bound of the Hausdorff dimension of the sets of vectors $(x_1, \\ldots, x_d)\\in [0,1)^d$ with large Weyl sums, namely of vectors for which $$ \\left| \\sum_{n=1}^{N}\\exp(2\\pi i (x_1 n+\\ldots +x_d n^{d})) \\right| \\ge N^{\\alpha} $$ for infinitely many integers $N \\ge 1$. Here we obtain an upper bound for the Hausdorff dimension of these exceptional sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T04:03:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L15",
      "28A78",
      "28A80"
    ],
    "keywords": [
      "hausdorff dimension",
      "large values",
      "large weyl sums",
      "exceptional sets",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}