# Kummer’s Lemma and Cyclotomic Units

The attached link is a group project underwent in Analytic Number Theory class in Carleton College: Kummer. The course was offered by Rafe Jones in Winter 2014.

It proves Kummer’s Lemma, that is “Every unit of $\mathbb{Z}[\zeta_p]$ is of the form of $r\zeta_p^g$ where $r \in \mathbb{R}$ and $g \in \mathbb{Z}$.” Plus, it introduces Cyclotomic units and presents an example.