Asymptotics for 6-torsion and D₆-extensions

2025/12/26 by Peter Koymans, Koymans, Peter, Robert J. Lemke Oliver +5
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.2512.21920

openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average 6-torsion of the class group of quadratic number fields. We also prove Malle's conjecture for Galois D₆-extensions.

Citations

• Malle's Conjecture for Galois octic fields over \mathbb Q
• Inductive methods for counting number fields
• Malle's conjecture and Brauer groups of stacks
• 6-torsion and integral points on quartic threefolds
• Averages of multiplicative functions along equidistributed sequences
• The average size of 3-torsion in class groups of 2-extensions
• Improved error estimates for the Davenport-Heilbronn theorems
• Subconvexity of Shintani's zeta function
• Uniform bounds for lattice point counting and partial sums of zeta functions
• On the Davenport-Heilbronn theorems and second order terms
• The density of discriminants of quintic rings and fields

Related

• Average bounds for the ℓ-torsion in class groups of cyclic extensions
• A geometric approach to the Cohen-Lenstra heuristics
• 6-torsion and integral points on quartic threefolds
• ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group
• Asymptotics of number fields and the Cohen--Lenstra heuristics