Minimal relative units of the cyclotomic $\mathbb Z_2$-extension

Tomokazu Kashio, Hyuga Yoshizaki

Published 2021-07-19Version 1

We study minimal relative units of each layer of the $\mathbb Z_2$-extension over $\mathbb Q$. Here ``minimal'' means that $\mathrm{Tr}\, \epsilon^2$ takes the minimum value other than $\epsilon=\pm 1$. We formulate a conjecture on minimal relative units and prove some partial results. We also study a relation to Weber's class number problem for low layers.