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Corpus ID: 219981353

Counting quintic fields with genus number one

@article{McGown2020CountingQF,
title={Counting quintic fields with genus number one},
author={Kevin J. McGown and Frank Thorne and Amanda Tucker},
journal={arXiv: Number Theory},
year={2020}
}

We prove several results concerning genus numbers of quintic fields: we compute the proportion of quintic fields with genus number one; we prove that a positive proportion of quintic fields have arbitrarily large genus number; and we compute the average genus number of quintic fields. All of these results also hold when restricted to $S_5$-quintic fields only.

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