Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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

Author(s): Ku-Young Chang; Soun-Hi Kwon.
Journal: Math. Comp. 72 (2003), 1003-1017.
MSC (2000): Primary 11R29; Secondary 11R21
Posted: 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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