• Corpus ID: 119127997

Statistics of genus numbers of cubic fields

@article{McGown2016StatisticsOG,
  title={Statistics of genus numbers of cubic fields},
  author={Kevin J. McGown and Amanda Tucker},
  journal={arXiv: Number Theory},
  year={2016}
}
We prove that approximately $96.23\%$ of cubic fields, ordered by discriminant, have genus number one, and we compute the exact proportion of cubic fields with a given genus number. We also compute the average genus number. Finally, we show that a positive proportion of totally real cubic fields with genus number one fail to be norm-Euclidean. 
4 Citations
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