{
  "id": "1509.04188",
  "version": "v1",
  "published": "2015-09-14T16:37:39.000Z",
  "updated": "2015-09-14T16:37:39.000Z",
  "title": "How far can you see in a forest?",
  "authors": [
    "Faustin Adiceam"
  ],
  "comment": "This is an extended version of a paper to appear",
  "categories": [
    "math.NT"
  ],
  "abstract": "We address a visibility problem posed by Solomon & Weiss. More precisely, in any dimension $n := d + 1 \\ge 2$, we construct a forest $\\F$ with finite density satisfying the following condition : if $\\e > 0$ denotes the radius common to all the trees in $\\F$, then the visibility $\\V$ therein satisfies the estimate $\\V(\\e) = O(\\e^{-2d-\\eta})$ for any $\\eta > 0$, no matter where we stand and what direction we look in. The proof involves Fourier analysis and sharp estimates of exponential sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-14T16:37:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J71",
      "11J25",
      "11L03",
      "11L07",
      "11Z05",
      "51N20"
    ],
    "keywords": [
      "exponential sums",
      "visibility problem",
      "sharp estimates",
      "fourier analysis",
      "radius common"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}