The distribution of $H_{8}$extensions of quadratic fields
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 nonabelian CohenLenstra heuristics for unramified Gextensions of quadratic fields for G in a large class of 2groups, 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 arXiv:
 arXiv:1611.05595
 Bibcode:
 2016arXiv161105595A
 Keywords:

 Mathematics  Number Theory