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arXiv · 2001.05350

On Dirichlet biquadratic fields

Étienne Fouvry·Peter Koymans
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Abstract

We study the $4$-rank of the ideal class group of $K_n := \mathbb{Q}(\sqrt{-n}, \sqrt{n})$. Our main result is that for a positive proportion of the squarefree integers $n$ we have that the $4$-rank of $\text{Cl}(K_n)$ equals $\omega_3(n) - 1$, where $\omega_3(n)$ is the number of prime divisors of $n$ that are $3$ modulo $4$.

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Étienne Fouvry, Peter Koymans. 2020-01-15. On Dirichlet biquadratic fields. https://arxiv.org/abs/2001.05350

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