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arXiv · 1108.5597

The Distribution of Number Fields with Wreath Products as Galois Groups

Jürgen Klüners
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Abstract

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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Jürgen Klüners. 2011-08-29. The Distribution of Number Fields with Wreath Products as Galois Groups. https://arxiv.org/abs/1108.5597

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