Corpus ID: 119312205

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

@article{Alberts2016TheDO,
  title={The distribution of \$H_\{8\}\$-extensions of quadratic fields},
  author={Brandon Alberts and Jack Klys},
  journal={arXiv: Number Theory},
  year={2016}
}
  • Brandon Alberts, Jack Klys
  • Published 2016
  • Mathematics
  • arXiv: Number Theory
  • 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… CONTINUE READING

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