The 4-ranks of the class groups of Q(sqrt(-d)) and Q(sqrt(-d0 d)) are asymptotically independent, each with the Cohen-Lenstra-Gerth distribution.
On Hasse's Unit Index
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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 $d\leq X$ such that $Q(L) = 2$ is proportional to $X/\sqrt{\log X}$.
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Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields
The 4-ranks of the class groups of Q(sqrt(-d)) and Q(sqrt(-d0 d)) are asymptotically independent, each with the Cohen-Lenstra-Gerth distribution.