{
  "id": "math/0703504",
  "version": "v2",
  "published": "2007-03-16T22:11:27.000Z",
  "updated": "2007-10-11T12:50:27.000Z",
  "title": "Ubiquity of simplices in subsets of vector spaces over finite fields",
  "authors": [
    "Derrick Hart",
    "Alex Iosevich"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CA",
    "math.CO"
  ],
  "abstract": "We prove that a sufficiently large subset of the $d$-dimensional vector space over a finite field with $q$ elements, $ {\\Bbb F}_q^d$, contains a copy of every $k$-simplex. Fourier analytic methods, Kloosterman sums, and bootstrapping play an important role.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-10-11T12:50:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "dimensional vector space",
      "fourier analytic methods",
      "sufficiently large subset",
      "kloosterman sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3504H"
    }
  }
}