| KUČERA, Radan. The circular units and the Stickelberger ideal of a cyclotomic field revisited. Acta Arithmetica. Institute of Mathematics, Polish Academy of Sciences, 2016, vol. 174, No 3, p. 217-238. ISSN 0065-1036. Available from: https://dx.doi.org/10.4064/aa8009-4-2016. |
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@article{1349599,
author = {Kučera, Radan},
article_number = {3},
doi = {http://dx.doi.org/10.4064/aa8009-4-2016},
keywords = {Circular (cyclotomic) units; Stickelberger ideal; odd and even universal ordinary distributions; Ennola relations.},
language = {eng},
issn = {0065-1036},
journal = {Acta Arithmetica},
title = {The circular units and the Stickelberger ideal of a cyclotomic field revisited},
volume = {174},
year = {2016}
}
TY - JOUR
ID - 1349599
AU - Kučera, Radan
PY - 2016
TI - The circular units and the Stickelberger ideal of a cyclotomic field revisited
JF - Acta Arithmetica
VL - 174
IS - 3
SP - 217-238
EP - 217-238
PB - Institute of Mathematics, Polish Academy of Sciences
SN - 00651036
KW - Circular (cyclotomic) units
KW - Stickelberger ideal
KW - odd and even universal ordinary distributions
KW - Ennola relations.
N2 - 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.
ER -
KUČERA, Radan. The circular units and the Stickelberger ideal of a cyclotomic field revisited. \textit{Acta Arithmetica}. Institute of Mathematics, Polish Academy of Sciences, 2016, vol.~174, No~3, p.~217-238. ISSN~0065-1036. Available from: https://dx.doi.org/10.4064/aa8009-4-2016.
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