There are many different definitions of the group of circular units of a real abelian field. The aim of this paper is to study their relations in the special case of a compositum k of real quadratic fields such that -1 is not a square in the genus field K of k in the narrow sense. The reason why fields of this type are considered is as follows. In such a field it is possible to define a group C of units (slightly bigger than Sinnott's group of circular units) such that the Galois group acts on C/(±C²) trivially (see [K, Lemma 2]). Due to this key property we can easily compare different groups of circular units (see the conclusion of this paper).
@article{bwmeta1.element.bwnjournal-article-aav67i2p123bwm,
author = {Radan Ku\v cera},
title = {Different groups of circular units of a compositum of real quadratic fields},
journal = {Acta Arithmetica},
volume = {68},
year = {1994},
pages = {123-140},
zbl = {0807.11050},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav67i2p123bwm}
}
Radan Kučera. Different groups of circular units of a compositum of real quadratic fields. Acta Arithmetica, Tome 68 (1994) pp. 123-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav67i2p123bwm/
[000] [G] R. Gillard, Remarques sur les unités cyclotomiques et les unités elliptiques, J. Number Theory 11 (1979), 21-48. | Zbl 0405.12008
[001] [K] R. Kučera, On the Stickelberger ideal and circular units of a compositum of quadratic fields, preprint. | Zbl 0840.11044
[002] [L] G. Lettl, A note on Thaine's circular units, J. Number Theory 35 (1990), 224-226. | Zbl 0705.11064
[003] [S] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. | Zbl 0465.12001
[004] [W] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982. | Zbl 0484.12001