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 $4$.