Counting D₄-field extensions by multi-invariants

2025/07/16 by Hansen, Willem, Zanoli, Anna · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.12342

Abstract

We count the number of Galois extensions M/ℚ with fixed Galois group Gal(M/ℚ)=D₄ 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.

Citations

• Counting biquadratic number fields with quaternionic and dihedral extensions
• Malle's conjecture and Brauer groups of stacks
• Malle's conjecture with multiple invariants
• On the asymptotics of cubic fields ordered by general invariants
• The Batyrev-Manin conjecture for DM stacks
• Heights on stacks and a generalized Batyrev-Manin-Malle conjecture
• Beyond heights: slopes and distribution of rational points
• The Hasse Norm Principle For Biquadratic Extensions
• The number of quartic D₄-fields ordered by conductor
• Hauteurs et mesures de Tamagawa sur les variétés de Fano

Cited by

• Non-vanishing of Artin L-functions associated with D₄-quartic function fields ordered by conductor

Related

• Malle's conjecture with multiple invariants
• Counting C₂ \wr S₄ fields with a power saving error term
• Lower bounds for counting A₄-quartic fields
• Inductive methods for counting number fields
• Counting G-Extensions by Discriminant