# cyclotomic units

Let $L=\mathbb{Q}(\zeta_{m})$ be a cyclotomic extension of $\mathbb{Q}$ with $m$ chosen to be minimal. Then the ring of integers is given by $\mathbb{Z}(\zeta_{m})$, and we denote the group of units by $\mathcal{O}_{L}^{\times}$. The cyclotomic units are the elements of a subgroup $C$ of $\mathcal{O}_{L}^{\times}$ given by

 $\displaystyle\eta=\frac{\zeta_{m}^{r}-1}{\zeta_{m}^{s}-1}$

with $r$ and $s$ relatively prime to $m$.

Title cyclotomic units CyclotomicUnits 2013-03-22 14:12:36 2013-03-22 14:12:36 mathcam (2727) mathcam (2727) 5 mathcam (2727) Definition msc 11R18