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Febuary 2020 Quartic fields with large class numbers
Atsuki Umegaki, Yumiko Umegaki
Rocky Mountain J. Math. 50(1): 267-280 (Febuary 2020). DOI: 10.1216/rmj.2020.50.267

Abstract

We show that there exist infinitely many quartic number fields K with large class numbers such that KQ 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 Q of degree 4 with large class numbers. We consider all the other cases of quartic Galois extensions.

Citation

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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

Information

Received: 12 October 2018; Revised: 10 June 2019; Accepted: 17 July 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201567
MathSciNet: MR4092557
Digital Object Identifier: 10.1216/rmj.2020.50.267

Subjects:
Primary: 11R16, 11R29

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 1 • Febuary 2020
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