22 citations · 33 across the 4 of their papers we have counts for
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What is the probability that a random integral quadratic form in variables has an integral zero?
M. Bhargava, J. E. Cremona, T. A. Fisher +2
We show that the density of quadratic forms in variables over that are isotropic is a rational function of , where the rational function is independent of ,…
A majority of elliptic curves over satisfy the Birch and Swinnerton-Dyer conjecture
Manjul Bhargava, Christopher Skinner, Wei Zhang
We prove that a majority (in fact, ) of all elliptic curves over , when ordered by height, satisfy the Birch and Swinnerton-Dyer rank conjecture.
Arithmetic invariant theory
Manjul Bhargava, Benedict H. Gross
Let be a field, let be a reductive algebraic group over , and let be a linear representation of . Geometric invariant theory involves the study of the -algebra…
The density of discriminants of quintic rings and fields
Manjul Bhargava
We determine, asymptotically, the number of quintic fields having bounded discriminant. Specifically, we prove that the asymptotic number of quintic fields having absolute discrimi…