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 ${𝒪}_L^{\times }$. The cyclotomic units are the elements of a subgroup $C$ of ${𝒪}_L^{\times }$ given by

$\eta ={\displaystyle \frac{{\zeta }_m^r-1}{{\zeta }_m^s-1}}$

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

Title	cyclotomic units
Canonical name	CyclotomicUnits
Date of creation	2013-03-22 14:12:36
Last modified on	2013-03-22 14:12:36
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	5
Author	mathcam (2727)
Entry type	Definition
Classification	msc 11R18