Counting quintic fields with genus number one
Number Theory
2023-07-28 v2
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 -quintic fields only.
Keywords
Cite
@article{arxiv.2006.12991,
title = {Counting quintic fields with genus number one},
author = {Kevin J. McGown and Frank Thorne and Amanda Tucker},
journal= {arXiv preprint arXiv:2006.12991},
year = {2023}
}
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7 pages