{
  "id": "2005.01211",
  "version": "v1",
  "published": "2020-05-03T23:47:52.000Z",
  "updated": "2020-05-03T23:47:52.000Z",
  "title": "Transcendence of $πr$ or $\\wp(ω_1 r)$",
  "authors": [
    "Yukitaka Abe"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\wp $ be a Weierstrass $\\wp $-function with algebraic $g_2$ and $g_3$, whose fundamental periods $\\omega _1, \\omega _2$ satisfy ${\\rm Im}(\\omega _1) = 0$. We show that $\\pi r$ or $\\wp(\\omega _1 r)$ is transcendental for any non-zero real number $r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-03T23:47:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transcendence",
      "non-zero real number",
      "fundamental periods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}