Statistics of genus numbers of cubic fields
Number Theory
2017-01-02 v2
Abstract
We prove that approximately 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.
Cite
@article{arxiv.1611.07088,
title = {Statistics of genus numbers of cubic fields},
author = {Kevin J. McGown and Amanda Tucker},
journal= {arXiv preprint arXiv:1611.07088},
year = {2017}
}