{
  "id": "1608.06401",
  "version": "v1",
  "published": "2016-08-23T07:00:35.000Z",
  "updated": "2016-08-23T07:00:35.000Z",
  "title": "Distinct distances on regular varieties over finite fields",
  "authors": [
    "Pham Van Thang",
    "Do Duy Hieu"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset $\\mathcal{E}$ in a regular variety satisfies $|\\mathcal{E}|\\gg q^{\\frac{d-1}{2}+\\frac{1}{k-1}}$, then $\\Delta_{k, F}(\\mathcal{E})\\supseteq \\mathbb{F}_q\\setminus \\{0\\}$ for some certain families of polynomials $F(\\mathbf{x})\\in \\mathbb{F}_q[x_1, \\ldots, x_d]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-23T07:00:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite fields",
      "distinct distances",
      "regular variety satisfies",
      "polynomials",
      "generalized versions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}