The Distribution of Number Fields with Wreath Products as Galois Groups

Details The Distribution of Number Fields with Wreath Products as Galois Groups The Distribution of Number Fields with Wreath Products as Galois Groups

2011-08-29

arxiv.org/abs/1108.5597v1

Mathematics

Number Theory

Scientific paper

Let $G$ be a wreath product of the form $C_2 \wr H$, where $C_2$ 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.

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