M. Bhargava

activity

20242026

collaborators

5 papers

math.NT2026

Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces

Manjul Bhargava, Arul Shankar, Xiaoheng Wang

We develop geometry-of-numbers methods to count orbits in prehomogeneous vector spaces having bounded invariants over any global field. As our primary example, we apply these techn…

math.NT2026

The existence of infinitely many cubic fields with class group of exact 2-rank 1

Manjul Bhargava, Arul Shankar, Artane Siad +1

We show that infinitely many cubic fields have class group of 2-rank 1.

math.NT2025

The second moment of the size of the $2$ -class group of monogenized cubic fields

Manjul Bhargava, Arul Shankar, Ashvin Swaminathan

We prove that when totally real (resp., complex) monogenized cubic number fields are ordered by height, the second moment of the size of the $2$ -class group is at most $3$ (resp.,…

math.NT2024

A proof of van der Waerden's Conjecture on random Galois groups of polynomials

Manjul Bhargava

Of the $(2 H + 1)^{n}$ monic integer polynomials $f (x) = x^{n} + a_{1} x^{n - 1} + \dots + a_{n}$ with $max {∣ a_{1} ∣, \dots, ∣ a_{n} ∣} \leq H$ , how many have associated Galois group that is not the full sy…

math.NT2024

Integers expressible as the sum of two rational cubes

Levent AlpÃ¶ge, Manjul Bhargava, Ari Shnidman

We prove that a positive proportion of integers are expressible as the sum of two rational cubes, and a positive proportion are not so expressible, thus proving a conjecture of Dav…