{
  "id": "1610.03172",
  "version": "v1",
  "published": "2016-10-11T03:45:54.000Z",
  "updated": "2016-10-11T03:45:54.000Z",
  "title": "Pinned algebraic distances determined by Cartesian products in $\\mathbb{F}_p^2$",
  "authors": [
    "Giorgis Petridis"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $p$ be an odd prime and $A \\subseteq \\mathbb{F}_p$ be a subset of the finite field with $p$ elements. We show that $A \\times A \\subseteq \\mathbb{F}_p^2$ determines at least a constant multiple of $\\min\\{p, |A|^{3/2}\\}$ distinct pinned algebraic distances.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T03:45:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian products",
      "distinct pinned algebraic distances",
      "odd prime",
      "finite field",
      "constant multiple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}