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1
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Different groups of circular units of a compositum of real quadratic fields

100%
Kučera R.
Acta Arithmetica
|
1994
|
tom 67
|
nr 2
123-140
EN
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).
2
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On annihilators of the class group of an imaginary compositum of quadratic fields

100%
Kučera R.
Acta Arithmetica
|
2010
|
tom 143
|
nr 3
257-269
3
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The circular units and the Stickelberger ideal of a cyclotomic field revisited

100%
Kučera R.
Acta Arithmetica
|
2016
|
tom 174
|
nr 3
217-238
EN
The aim of this paper is a new construction of bases of the group of circular units and of the Stickelberger ideal for a family of abelian fields containing all cyclotomic fields, namely for any compositum of imaginary abelian fields, each ramified only at one prime. In contrast to the previous papers on this topic our approach consists in an explicit construction of Ennola relations. This gives an explicit description of the torsion parts of odd and even universal ordinary distributions, but it also allows us to give a shorter proof that the given set of elements is a basis. Moreover we obtain a presentation of the group of circular numbers for any field in the above mentioned family.
4
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On a conjecture concerning minus parts in the style of Gross

64%
Greither C., Kučera R.
Acta Arithmetica
|
2008
|
tom 132
|
nr 1
1-48
5
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Racines d'unités cyclotomiques et divisibilité du nombre de classes d'un corps abélien réel

51%
Greither C., Hachami S., Kučera R.
Acta Arithmetica
|
2000-2001
|
tom 96
|
nr 3
247-259
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