Dihedral and cyclic extensions with large class numbers
@article{Cho2012DihedralAC, 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}, year={2012}, volume={24}, pages={583-603} }
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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