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math.NT2022★ 4 cited
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…
math.NT2022
On the asymptotics of cubic fields ordered by general invariants
Arul Shankar, Frank Thorne
In this article, we introduce a class of invariants of cubic fields termed generalized discriminants. We then obtain asymptotics for the families of cubic fields ordered by these i…
math.NT2022★ 1 cited
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…