{
  "id": "1601.06378",
  "version": "v1",
  "published": "2016-01-24T13:00:25.000Z",
  "updated": "2016-01-24T13:00:25.000Z",
  "title": "Ternary quadratic forms and linear combination of three triangular numbers",
  "authors": [
    "Zhi-Hong Sun"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Bbb Z$ and $\\Bbb N$ be the set of integers and the set of positive integers, respectively. For $a,b,c,n\\in\\Bbb N$ let $N(a,b,c;n)$ be the number of representations of $n$ by $ax^2+by^2+cz^2$, and let $t(a,b,c;n)$ be the number of representations of $n$ by $ax(x-1)/2+by(y-1)/2+cz(z-1)/2 $ $(x,y,z\\in\\Bbb Z$). In this paper, by using Ramanujan's theta functions we reveal some connections between $t(a,b,c;n)$ and $N(a,b,c;n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-24T13:00:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30B10",
      "33E20",
      "11D85",
      "11E25"
    ],
    "keywords": [
      "ternary quadratic forms",
      "linear combination",
      "triangular numbers",
      "ramanujans theta functions",
      "representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160106378S"
    }
  }
}