Counting $D_4$-field extensions by multi-invariants
Number Theory
2025-07-17 v1
Abstract
We count the number of Galois extensions with fixed Galois group 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.
Keywords
Cite
@article{arxiv.2507.12342,
title = {Counting $D_4$-field extensions by multi-invariants},
author = {Willem Hansen and Anna Zanoli},
journal= {arXiv preprint arXiv:2507.12342},
year = {2025}
}
Comments
28 pages, comments welcome