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arXiv · 2507.12342

Counting $D_4$-field extensions by multi-invariants

Willem Hansen·Anna Zanoli
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Abstract

We count the number of Galois extensions $M/\mathbb{Q}$ with fixed Galois group $\text{Gal}(M/\mathbb{Q})=D_4$ ordered by multi-invariants introduced by Gundlach. We verify the asymptotic behavior predicted by Gundlach's version of Malle's conjecture. We compare the leading constant to recent predictions by Loughran and Santens.

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Willem Hansen, Anna Zanoli. 2025-07-16. Counting $D_4$-field extensions by multi-invariants. https://arxiv.org/abs/2507.12342

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