{
  "id": "1912.12930",
  "version": "v1",
  "published": "2019-12-30T13:59:37.000Z",
  "updated": "2019-12-30T13:59:37.000Z",
  "title": "Representations of finite number of quadratic forms with same rank",
  "authors": [
    "Daejun Kim",
    "Byeong-Kweon Oh"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $m, n$ be positive integers with $m\\le n$. Let $\\kappa(m,n)$ be the largest integer $k$ such that for any (positive definite and integral) quadratic forms $f_1,\\ldots,f_k$ of rank $m$, there exists a quadratic form of rank $n$ that represents $f_i$ for any $i$ with $1\\le i \\le k$. In this article, we determine the number $\\kappa(m,n)$ for any integer $m$ with $1\\le m\\le 8$, except for the cases when $(m,n)=(3,5)$ and $(4,6)$. In the exceptional cases, it will be proved that $1\\le \\kappa(3,5), \\ \\kappa(4,6)\\le 2$. We also discuss some related topics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-30T13:59:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic form",
      "finite number",
      "representations",
      "largest integer",
      "exceptional cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}