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

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 $ω_3(n) - 1$, where $ω_3$ is the number of prime divisors of $n$ that are $3$ modulo $4$.

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