{
  "id": "2203.00731",
  "version": "v1",
  "published": "2022-03-01T20:36:42.000Z",
  "updated": "2022-03-01T20:36:42.000Z",
  "title": "A lower bound on the proportion of modular elliptic curves over Galois CM fields",
  "authors": [
    "Zachary Feng"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We calculate an explicit lower bound on the proportion of elliptic curves that are modular over any Galois CM field not containing $\\zeta_5$. Applied to imaginary quadratic fields, this proportion is at least $2/5$. Applied to cyclotomic fields $\\mathbb{Q}(\\zeta_n)$ with $5\\nmid n$, this proportion is at least $1-\\varepsilon$ with only finitely many exceptions of $n$, for any choice of $\\varepsilon > 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-01T20:36:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois cm field",
      "modular elliptic curves",
      "proportion",
      "explicit lower bound",
      "imaginary quadratic fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}