2 citations · 3 across the 3 of their papers we have counts for
3 papers
math.NT2026
Geometry-of-numbers methods over global fields II: Coregular representations
Manjul Bhargava, Arul Shankar, Xiaoheng Wang
We develop geometry-of-numbers methods to count orbits in coregular vector spaces having bounded invariants over any global field. We apply these techniques to bound the average ra…
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.NT2020★ 2 cited
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 $…