{
  "id": "math/0611619",
  "version": "v1",
  "published": "2006-11-20T20:59:18.000Z",
  "updated": "2006-11-20T20:59:18.000Z",
  "title": "Semidirect Products and Functional Equations for Quantum Multiplication",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT",
    "math.QA"
  ],
  "abstract": "The quantum integer [n]_q is the polynomial 1 + q + q^2 + ... + q^{n-1}, and the sequence of polynomials { [n]_q }_{n=1}^{\\infty} is a solution of the functional equation f_{mn}(q) = f_m(q)f_n(q^m). In this paper, semidirect products of semigroups are used to produce families of functional equations that generalize the functional equation for quantum multiplication.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-20T20:59:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B05",
      "11T22",
      "30B10",
      "81R50",
      "11B13"
    ],
    "keywords": [
      "functional equation",
      "quantum multiplication",
      "semidirect products",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11619N"
    }
  }
}