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arXiv · 2006.12991

Counting quintic fields with genus number one

Kevin J. McGown·Frank Thorne·Amanda Tucker
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Abstract

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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Kevin J. McGown, Frank Thorne, Amanda Tucker. 2023-07-27. Counting quintic fields with genus number one. https://arxiv.org/abs/2006.12991

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