{
  "id": "2107.08587",
  "version": "v1",
  "published": "2021-07-19T02:41:25.000Z",
  "updated": "2021-07-19T02:41:25.000Z",
  "title": "Minimal relative units of the cyclotomic $\\mathbb Z_2$-extension",
  "authors": [
    "Tomokazu Kashio",
    "Hyuga Yoshizaki"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study minimal relative units of each layer of the $\\mathbb Z_2$-extension over $\\mathbb Q$. Here ``minimal'' means that $\\mathrm{Tr}\\, \\epsilon^2$ takes the minimum value other than $\\epsilon=\\pm 1$. We formulate a conjecture on minimal relative units and prove some partial results. We also study a relation to Weber's class number problem for low layers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-19T02:41:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R27",
      "11R29",
      "11R18",
      "11Y40"
    ],
    "keywords": [
      "cyclotomic",
      "webers class number problem",
      "study minimal relative units",
      "minimum value",
      "low layers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}