The Distribution of Number Fields with Wreath Products as Galois Groups

2011/08/29 by Klüners, Jürgen · 2 citations
#11R16 #11R29 #11R32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1108.5597

Abstract

Let G be a wreath product of the form C₂ \wr H, where C₂ is the cyclic group of order 2. Under mild conditions for H we determine the asymptotic behavior of the counting functions for number fields K/k with Galois group G and bounded discriminant. Those counting functions grow linearly with the norm of the discriminant and this result coincides with a conjecture of Malle. Up to a constant factor these groups have the same asymptotic behavior as the conjectured one for symmetric groups.

Cited by

• Counting C₂ \wr S₄ fields with a power saving error term
• A power-saving error term in counting C₂ \wr H extensions of an arbitrary base field parametrized by discriminants

Related

• Counting number fields whose Galois group is a wreath product of symmetric groups
• Counting nilpotent Galois extensions
• A counter example to Malle's conjecture on the asymptotics of discriminants
• Ordering of number fields and distribution of class groups
• The asymptotics of nilpotent Galois groups