A power-saving error term in counting C₂ \wr H extensions of an arbitrary base field parametrized by discriminants

2025/11/25 by Chakraborty, Arijit
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.19921

Abstract

We study Malle's conjecture for the group C₂ \wr H where H is a permutation group. Malle's conjecture for this case was proved by Jürgen Klüners in \citearXiv:1108.5597 under mild conditions for H. In this article, we provide an alternative method to obtain the explicit main term and a power-saving error term for C₂ \wr H extensions of an arbitrary number field. Furthermore, our method allows us to relax the assumptions for H.

Citations

• An improved error term for counting D₄-quartic fields
• Power-saving error terms for the number of D₄-quartic extensions over a number field ordered by discriminant
• Uniform bounds for lattice point counting and partial sums of zeta functions
• Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves
• The Distribution of Number Fields with Wreath Products as Galois Groups
• A counter example to Malle's conjecture on the asymptotics of discriminants

Related

• Counting C₂ \wr S₄ fields with a power saving error term
• Inductive methods for counting number fields
• A counter example to Malle's conjecture on the asymptotics of discriminants
• Power-saving error terms for the number of D₄-quartic extensions over a number field ordered by discriminant
• Lower bounds for counting A₄-quartic fields