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

Abstract

We study minimal relative units of each layer of the Z 2 -extension over Q. Here "minimal" means that Tr ǫ 2 takes the minimum value other than ǫ = ±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.