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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12342 |
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| _version_ | 1866912486150635520 |
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| author | Hansen, Willem Zanoli, Anna |
| author_facet | Hansen, Willem Zanoli, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting $D_4$-field extensions by multi-invariants Hansen, Willem Zanoli, Anna Number Theory 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. |
| title | Counting $D_4$-field extensions by multi-invariants |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.12342 |