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.
Publié le : 2001-11-14
Classification:
Quartic field,
fundamental unit system,
class number,
11R20,
11R27,
11R29,
11R11
@article{1148393008,
author = {Wang, Kunpeng},
title = {Fundamental unit system and class number of real bicyclic biquadratic number fields},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {77},
number = {10},
year = {2001},
pages = { 147-150},
language = {en},
url = {http://dml.mathdoc.fr/item/1148393008}
}
Wang, Kunpeng. Fundamental unit system and class number of real bicyclic biquadratic number fields. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp. 147-150. http://gdmltest.u-ga.fr/item/1148393008/