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Dihedral and cyclic extensions with large class numbers

Peter J. Cho; Henry H. Kim — 2012

Journal de Théorie des Nombres de Bordeaux

This paper is a continuation of []. 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 $D_{n}$ , $n = 3, 4, 5$ , and cyclic groups $C_{n}$ , $n = 4, 5, 6$ . 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 $L$ -functions are zero free...

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