Publication details

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



Year of publication 2016
Type Article in Periodical
Magazine / Source Acta Arithmetica
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Circular (cyclotomic) units; Stickelberger ideal; odd and even universal ordinary distributions; Ennola relations.
Description 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.
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