Statistics of genus numbers of cubic fields

2016/11/21 by McGown, Kevin J., Tucker, Amanda · 3 citations
#11A05 #11R16 #11R29 #11R45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.07088

Abstract

We prove that approximately 96.23% of cubic fields, ordered by discriminant, have genus number one, and we compute the exact proportion of cubic fields with a given genus number. We also compute the average genus number. Finally, we show that a positive proportion of totally real cubic fields with genus number one fail to be norm-Euclidean.

Cited by

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

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