On the $4$-rank of class groups of Dirichlet biquadratic fields

Abstract

We show that for $100\%$ of the odd, squarefree integers $n>0$ the $4$-rank of $\text{Cl}(\mathbb{Q}(i,\sqrt{n}))$ is equal to ${\omega }_3(n)-1$, where ${\omega }_3$ is the number of prime divisors of $n$ that are $3$ modulo $4$.

25 pages