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@article{1106916,
author = {Bulant, Michal and Kučera, Radan},
article_number = {9},
doi = {http://dx.doi.org/10.1016/j.jnt.2013.03.009},
keywords = {Real abelian field; Zp-extension; Group of circular units},
language = {eng},
issn = {0022-314X},
journal = {Journal of Number Theory},
title = {On a modification of the group of circular units of a real abelian field},
volume = {133},
year = {2013}
}
TY - JOUR
ID - 1106916
AU - Bulant, Michal - Kučera, Radan
PY - 2013
TI - On a modification of the group of circular units of a real abelian field
JF - Journal of Number Theory
VL - 133
IS - 9
SP - 3138 - 3148
EP - 3138 - 3148
PB - Elsevier
SN - 0022314X
KW - Real abelian field
KW - Zp-extension
KW - Group of circular units
N2 - For a real abelian field K, Sinnott's group of circular units C_K is a subgroup of finite index in the full group of units E_K playing an important role in Iwasawa theory. Let K_infty/K be the cyclotomic Z(p)-extension of K, and h(Kn) be the class number of K_n, the n-th layer in K_infty/K. Then for p<>2 and n going to infinity, the p-parts of the quotients [E_Kn : C_Kn]/h(Kn) stabilize. Unfortunately this is not the case for p=2, when the group C_1K of all units of K, whose squares belong to C_K, is usually used instead of C_K. But C_1K is better only for index formula purposes, not having the other nice properties of C_K. The main aim of this paper is to offer another alternative to C_K which can be used in cyclotomic Z(p)-extensions even for p=2 still keeping almost all nice properties of C_K.
ER -
BULANT, Michal and Radan KUČERA. On a modification of the group of circular units of a real abelian field. \textit{Journal of Number Theory}. Elsevier, 2013, vol.~133, No~9, p.~3138 - 3148. ISSN~0022-314X. Available from: https://dx.doi.org/10.1016/j.jnt.2013.03.009.
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