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The circular units and the Stickelberger ideal of a cyclotomic field revisited

Volume 174 / 2016

Radan Kučera Acta Arithmetica 174 (2016), 217-238 MSC: Primary 11R18. DOI: 10.4064/aa8009-4-2016 Published online: 12 July 2016

Abstract

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.

Authors

  • Radan KučeraDepartment of Mathematics and Statistics
    Faculty of Science
    Masaryk University
    Kotlářská 2
    611 37 Brno, Czech Republic
    e-mail

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