cyclotomic units
CyclotomicUnits
2004-02-27 15:36:58
2004-03-02 17:16:52
Definition
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Let $L=\Q(\zeta_m)$ be a cyclotomic extension of $\Q$ with $m$ chosen to be minimal. Then the ring of integers is given by $\Z(\zeta_m)$, and we denote the group of units by $\mc{O}_L^\times$. \emph{The cyclotomic units} are the elements of a subgroup $C$ of $\mc{O}_L^\times$ given by
\begin{align*}
\eta=\frac{\zeta_m^r-1}{\zeta_m^s-1}
\end{align*}
with $r$ and $s$ relatively prime to $m$.