63 citations · 557 across the 46 of their papers we have counts for
7 papers · 1 filter
Galois groups of random integer polynomials and van der Waerden's Conjecture
Manjul Bhargava
Of the monic integer polynomials with , how many have associated Galois group that is not the full sy…
On the number of monogenizations of a quartic order
Manjul Bhargava
We show that an order in a quartic field has fewer than essentially different generators as a -algebra (and fewer than if the discriminant of the order is s…
The second moment of the size of the -Selmer group of elliptic curves
Manjul Bhargava, Arul Shankar, Ashvin Swaminathan
In this paper, we prove that when elliptic curves over are ordered by height, the second moment of the size of the -Selmer group is at most . This confirms a co…
Hermite equivalence of polynomials
Manjul Bhargava, Jan-Hendrik Evertse, Kálmán Győry +2
In this paper, we resurrect a long-forgotten notion of equivalence for univariate polynomials with integral coefficients introduced by Hermite in the 1850s. We show that the Hermit…
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…
Improved error estimates for the Davenport-Heilbronn theorems
Manjul Bhargava, Takashi Taniguchi, Frank Thorne
We improve the error terms in the Davenport-Heilbronn theorems on counting cubic fields to . This improves on separate and independent results of the authors and Sh…