Kevin J. McGown, Amanda Tucker
Published 2016-11-21Version 1
We prove that approximately $96.23\%$ of cubic fields when ordered by discriminant have genus number one. We compute in general the exact proportion of cubic fields with a given genus number, as well as 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.
A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so
Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
Classifying multiplets of totally real cubic fields
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