Proceedings of the Japan Academy, Series A, Mathematical Sciences

Fundamental unit system and class number of real bicyclic biquadratic number fields

Kunpeng Wang

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Abstract

In this note, we study the unit groups and class numbers of three classes of bicyclic biquadratic number fields. Following Wada and Zhang's methods, the unit group and class number of a bicyclic biquadratic number field can be represented by the fundamental units and class numbers of their quadratic subgroups. The reason why this method works in our case is that the fundamental unit of the quadratic subfields of our bicyclic biquadratic fields can be determined explicitly.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 9 (2001), 147-150.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393008

Digital Object Identifier
doi:10.3792/pjaa.77.147

Mathematical Reviews number (MathSciNet)
MR1869110

Zentralblatt MATH identifier
1011.11071

Subjects
Primary: 11R20: Other abelian and metabelian extensions 11R27: Units and factorization 11R29: Class numbers, class groups, discriminants 11R11: Quadratic extensions

Keywords
Quartic field fundamental unit system class number

Citation

Wang, Kunpeng. Fundamental unit system and class number of real bicyclic biquadratic number fields. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 9, 147--150. doi:10.3792/pjaa.77.147. https://projecteuclid.org/euclid.pja/1148393008


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References

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