On Hasse's Unit Index

Abstract

We study the distribution of Hasse's unit index $Q(L)$ for the CM-fields $L=\mathbb{Q}(\sqrt{d},\sqrt{-1})$ as $d$ varies among positive squarefree integers. We prove that the number of $d\le X$ such that $Q(L)=2$ is proportional to $X/\sqrt{\log X}$.

11 pages