63 citations · 557 across the 46 of their papers we have counts for
4 papers · 1 filter
Integers expressible as the sum of two rational cubes
Levent Alpöge, 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…
On average sizes of Selmer groups and ranks in families of elliptic curves having marked points
Manjul Bhargava, Wei Ho
We determine average sizes/bounds for the - and -Selmer groups in various families of elliptic curves with marked points, thus confirming several cases of the Poonen--Rains h…
Squarefree values of polynomial discriminants II
Manjul Bhargava, Arul Shankar, Xiaoheng Wang
We determine the density of integral binary forms of given degree that have squarefree discriminant, proving for the first time that the lower density is positive. Furthermore, we…
An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree
Manjul Bhargava, Arul Shankar, Xiaoheng Wang
We prove an improvement on Schmidt's upper bound on the number of number fields of degree and absolute discriminant less than X for . We carry this out by imp…