{
  "id": "1508.02691",
  "version": "v1",
  "published": "2015-08-11T19:03:38.000Z",
  "updated": "2015-08-11T19:03:38.000Z",
  "title": "Pairs of dot products in finite fields and rings",
  "authors": [
    "David Covert",
    "Steven Senger"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We obtain bounds on the number of triples that determine a given pair of dot products arising in a vector space over a finite field or a module over the set of integers modulo a power of a prime. More precisely, given $E\\subset \\mathbb F_q^d$ or $\\mathbb Z_q^d$, we provide bounds on the size of the set \\[\\left\\{(u,v,w)\\in E \\times E \\times E : u\\cdot v = \\alpha, u \\cdot w = \\beta \\right\\}\\] for units $\\alpha$ and $\\beta$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-11T19:03:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "vector space",
      "integers modulo",
      "dot products arising"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150802691C"
    }
  }
}