Dihedral and cyclic extensions with large class numbers

  title={Dihedral and cyclic extensions with large class numbers},
  author={Peter J. Cho and Henry H. Kim},
  journal={Journal de Theorie des Nombres de Bordeaux},
This paper is a continuation of [2]. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups Dn, n = 3, 4, 5, and cyclic groups Cn, n = 4, 5, 6. We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modification of zero density result of Kowalski-Michel, we choose subfamilies such that the corresponding… 
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