English

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 S5S_5-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}
}

Comments

7 pages

R2 v1 2026-06-23T16:33:21.336Z