M. Bhargava

activity

20102026

most citedThe average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point

63 citations · 557 across the 46 of their papers we have counts for

collaborators

Showing 2015 · math.NTShow all

2 papers · 2 filters

math.NT2015★ 21 cited

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.NT2015★ 7 cited

What is the probability that a random integral quadratic form in $n$ variables has an integral zero?

M. Bhargava, J. E. Cremona, T. A. Fisher +2

We show that the density of quadratic forms in $n$ variables over $Z_{p}$ that are isotropic is a rational function of $p$ , where the rational function is independent of $p$ ,…

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

What is the probability that a random integral quadratic form in n variables has an integral zero?

What is the probability that a random integral quadratic form in $n$ variables has an integral zero?