1 citations · 1 across the 2 of their papers we have counts for
3 papers
math.NT2025★ 1 cited
Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field
Levent Alpöge, Manjul Bhargava, Wei Ho +1
We show that for any quadratic extension of number fields , there exists an abelian variety of positive rank whose rank does not grow upon base change to . This resul…
math.NT2021
A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so
Levent Alpöge, Manjul Bhargava, Ari Shnidman
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 cub…
math.NT2020
A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so
Levent Alpöge, Manjul Bhargava, Ari Shnidman
We show that a positive proportion of cubic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof involves the comparison of -descent and $…