{
  "id": "2405.08383",
  "version": "v1",
  "published": "2024-05-14T07:30:11.000Z",
  "updated": "2024-05-14T07:30:11.000Z",
  "title": "Faithful Artin induction and the Chebotarev density theorem",
  "authors": [
    "Robert J. Lemke Oliver",
    "Alexander Smith"
  ],
  "comment": "50 pages",
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number field F, almost all are subject to a strong effective version of the Chebotarev density theorem. We use this version of the Chebotarev density theorem to deduce several consequences for class groups in families of number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-14T07:30:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chebotarev density theorem",
      "faithful artin induction",
      "number field",
      "vector space",
      "class groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}