Statistics of genus numbers of cubic fields
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 wit...
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| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.1611.07088 |