{
  "id": "2102.12187",
  "version": "v1",
  "published": "2021-02-24T10:23:56.000Z",
  "updated": "2021-02-24T10:23:56.000Z",
  "title": "Classifying multiplets of totally real cubic fields",
  "authors": [
    "Daniel C. Mayer"
  ],
  "comment": "41 pages, 34 tables, 10 figures. arXiv admin note: substantial text overlap with arXiv:1904.06148",
  "categories": [
    "math.NT"
  ],
  "abstract": "The number of non-isomorphic cubic fields L sharing a common discriminant d(L) = d is called the multiplicity m = m(d) of d. For an assigned value of d, these fields are collected in a multiplet M(d) = (L(1) ,..., L(m)). In this paper, the information in all existing tables of totally real cubic number fields L with positive discriminants d(L) < 10000000 is extended by computing the differential principal factorization types tau(L) in (alpha1, alpha2, alpha3, beta1, beta2, gamma, delta1, delta2, epsilon) of the members L of each multiplet M(d) of non-cyclic fields, a new kind of arithmetical invariants which provide succinct information about ambiguous principal ideals and capitulation in the normal closures N of non-Galois cubic fields L. The classification is arranged with respect to increasing 3-class rank of the quadratic subfields K of the S3-fields N, and to ascending number of prime divisors of the conductor f of N/K. The Scholz conjecture concerning the distinguished index of subfield units (U(N) : U(0)) = 1 for ramified extensions N/K with conductor f > 1 is refined and verified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-24T10:23:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R37",
      "11R11",
      "11R16",
      "11R20",
      "11R27",
      "11R29",
      "11Y40"
    ],
    "keywords": [
      "totally real cubic fields",
      "classifying multiplets",
      "totally real cubic number fields",
      "non-isomorphic cubic fields",
      "common discriminant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}