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The class number one problem for some non-abelian normal CM-fields of degree 48

Authors: Ku-Young Chang and Soun-Hi Kwon
Journal: Math. Comp. 72 (2003), 1003-1017
MSC (2000): Primary 11R29; Secondary 11R21
Published electronically: October 17, 2002
MathSciNet review: 1954981
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Abstract: We prove that there is precisely one normal CM-field of degree 48 with class number one which has a normal CM-subfield of degree 16: the narrow Hilbert class field of $\mathbb{Q} (\sqrt{5}, \sqrt{101}, \theta )$ with $ \theta^3 - \theta^2 -5 \theta -1=0$.

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Additional Information

Ku-Young Chang
Affiliation: Information Security Basic Research Team, ETRI, 161 Kajong-dong, Yusong-Gu, 305-350, Taejon, Korea

Soun-Hi Kwon
Affiliation: Department of Mathematics Education, Korea University, 136-701, Seoul, Korea

Received by editor(s): March 24, 2000
Received by editor(s) in revised form: December 26, 2000, May 2, 2001, and September 5, 2001
Published electronically: October 17, 2002
Article copyright: © Copyright 2002 American Mathematical Society