{
  "id": "1910.04479",
  "version": "v1",
  "published": "2019-10-10T10:57:13.000Z",
  "updated": "2019-10-10T10:57:13.000Z",
  "title": "Remark on a Simple Proof of the Mean Value of $K_2(\\mathcal{O})$ in Function Fields",
  "authors": [
    "J. MacMillan"
  ],
  "comment": "6 pages; Comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathbb{F}_q$ denote a finite field of odd cardinality $q$, $\\mathbb{A}=\\mathbb{F}_q[T]$ the polynomial ring over $\\mathbb{F}_q$ and $k=\\mathbb{F}_q(T)$ the rational function field over $\\mathbb{F}_q$. In this paper, we compute the average value of the size of the group $K_2(\\mathcal{O}_{\\gamma D})$, where $\\mathcal{O}_{\\gamma D}$ denotes the integral closure of $\\mathbb{A}$ in $k(\\sqrt{\\gamma D})$, $D$ is a monic, square-free polynomial of even degree and $\\gamma$ is a fixed generator of $\\mathbb{F}_q^*$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-10T10:57:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M38",
      "11G20",
      "11M06",
      "13F30",
      "11R58",
      "14G10"
    ],
    "keywords": [
      "mean value",
      "simple proof",
      "rational function field",
      "odd cardinality",
      "finite field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}