Abstract
We show that a positive proportion of quartic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof builds on the corresponding result for cubic fields that we obtained in a previous work. Along the way, we also prove that a positive proportion of quartic rings of integers do not arise as the invariant order of an integral binary quartic form despite having no local obstruction.
Original language | English (US) |
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Pages (from-to) | 4037-4052 |
Number of pages | 16 |
Journal | Mathematische Annalen |
Volume | 388 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2024 |
All Science Journal Classification (ASJC) codes
- General Mathematics