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arXiv · 1611.05595

The distribution of $H_{8}$-extensions of quadratic fields

Brandon Alberts·Jack Klys
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Abstract

We compute all the moments of a normalization of the function which counts unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the quaternion group of order 8, and show that the values of this function determine a constant distribution. Furthermore we propose a similar modification to the non-abelian Cohen-Lenstra heuristics for unramified G-extensions of quadratic fields for G in a large class of 2-groups, which we conjecture will give finite moments which determine a distribution. Our method additionally can be used to determine the asymptotics of the unnormalized counting function, which we also do for unramified $H_{8}$-extensions.

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Brandon Alberts, Jack Klys. 2016-11-17. The distribution of $H_{8}$-extensions of quadratic fields. https://arxiv.org/abs/1611.05595

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