Counting quintic fields with genus number one

2020/06/23 by McGown, Kevin J., Thorne, Frank, Tucker, Amanda · 4 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.12991

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 S₅-quintic fields only.

Cited by

• Polynomial densities and Heilbronn's criterion
• Euclidean Algorithms for Ideal Classes in Biquadratic fields: A Genus-Theoretic Perspective
• Twisted Malle's Conjecture
• The average genus number for pure fields of prime degree

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