Levent Alpöge, Manjul Bhargava, Ari Shnidman
Published 2021-07-12Version 1
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.
Comments: 14 pages, comments welcome
A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so
An improved error term for $D_4$-quartic fields
The average sizes of two-torsion subgroups in quotients of class groups of cubic fields
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