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

Chang, Ku-Young; Kwon, Soun-Hi

doi:10.1090/S0025-5718-02-01443-6

The class number one problem for some non-abelian normal CM-fields of degree 48
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by Ku-Young Chang and Soun-Hi Kwon;

Math. Comp. 72 (2003), 1003-1017

DOI: https://doi.org/10.1090/S0025-5718-02-01443-6

Published electronically: October 17, 2002

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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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