Abstract
We show that there exist infinitely many quartic number fields with large class numbers such that is a Galois extension whose Galois group is isomorphic to a given finite group. Cho and Kim proved that there are infinitely many totally real cyclic extensions over of degree with large class numbers. We consider all the other cases of quartic Galois extensions.
Citation
Atsuki Umegaki. Yumiko Umegaki. "Quartic fields with large class numbers." Rocky Mountain J. Math. 50 (1) 267 - 280, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.267
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