{
  "id": "1401.3553",
  "version": "v1",
  "published": "2014-01-15T11:58:22.000Z",
  "updated": "2014-01-15T11:58:22.000Z",
  "title": "A note on the arithmetic properties of Stern Polynomials",
  "authors": [
    "Maciej Gawron"
  ],
  "comment": "9 pages, submitted",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We investigate the Stern polynomials defined by $B_0 ( t ) =0,B_1 ( t ) =1$, and for $n \\geq 2$ by the recurrence relations $B_{2n}( t) =tB_{n}( t) ,$ $B_{2n+1}( t) =B_n( t) +B_{n+1}( t) $. We prove that all possible rational roots of that polynomials are $0,-1,-1/2,-1/3$. We give complete characterization of $n$ such that $deg( B_n) = deg( B_{n+1}) $ and $deg( B_n) =deg( B_{n+1}) =deg( B_{n+2}) $. Moreover, we present some result concerning reciprocal Stern polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-15T11:58:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic properties",
      "result concerning reciprocal stern polynomials",
      "rational roots",
      "recurrence relations",
      "complete characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.3553G"
    }
  }
}