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

Radan Kučera. "The circular units and the Stickelberger ideal of a cyclotomic field revisited." Acta Arithmetica 174.3 (2016): 217-238. <http://eudml.org/doc/286232>.

@article{RadanKučera2016,
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.},
author = {Radan Kučera},
journal = {Acta Arithmetica},
keywords = {circular (cyclotomic) units; Stickelberger ideal; odd and even universal ordinary distributions; ennola relations},
language = {eng},
number = {3},
pages = {217-238},
title = {The circular units and the Stickelberger ideal of a cyclotomic field revisited},
url = {http://eudml.org/doc/286232},
volume = {174},
year = {2016},
}

TY - JOUR
AU - Radan Kučera
TI - The circular units and the Stickelberger ideal of a cyclotomic field revisited
JO - Acta Arithmetica
PY - 2016
VL - 174
IS - 3
SP - 217
EP - 238
AB - 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.
LA - eng
KW - circular (cyclotomic) units; Stickelberger ideal; odd and even universal ordinary distributions; ennola relations
UR - http://eudml.org/doc/286232
ER -