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VOL. 84 | 2020 Bicubic number fields with large class numbers
Yasuko Morita, Atsuki Umegaki, Yumiko Umegaki

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Abstract

For a given finite group $G$, the problem whether there exist infinitely many number fields $K$ with large class number and Galois group $\mathrm{Gal}(K/\boldsymbol{\mathrm{Q}}) \cong G$ is interesting and important. This problem was proved affirmatively for some groups $G$.

In this paper, we approach this problem by considering $h_KR_K$, where $h_K$ is the class number of $K$ and $R_K$ is the regulator of $K$. We prove that there exist infinitely many bicubic number fields $K$ with large $h_KR_K$. Moreover, we also prove generalization of the claim.

Information

Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283191

Digital Object Identifier: 10.2969/aspm/08410335

Subjects:
Primary: 11R29

Keywords: Class number

Rights: Copyright © 2020 Mathematical Society of Japan

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