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 2020Show all

3 papers · 1 filter

math.NT2020★ 4 cited

The mean number of 2-torsion elements in the class groups of $n$ -monogenized cubic fields

Manjul Bhargava, Jonathan Hanke, Arul Shankar

We prove that, on average, the monogenicity or $n$ -monogenicity of a cubic field has an altering effect on the behavior of the 2-torsion in its class group.

math.NT2020

The local-global principle for integral points on stacky curves

Manjul Bhargava, Bjorn Poonen

We construct a stacky curve of genus $1/2$ (i.e., Euler characteristic $1$ ) over $Z$ that has an $R$ -point and a $Z_{p}$ -point for every prime $p$ but no $…

math.NT2020★ 3 cited

The proportion of genus one curves over $Q$ defined by a binary quartic that everywhere locally have a point

Manjul Bhargava, John Cremona, Tom Fisher

We consider the proportion of genus one curves over $Q$ of the form $z^{2} = f (x, y)$ where $f (x, y) \in Z [x, y]$ is a binary quartic form (or more generally of the form $…

The mean number of 2-torsion elements in the class groups of n-monogenized cubic fields

The local-global principle for integral points on stacky curves

The proportion of genus one curves over Q defined by a binary quartic that everywhere locally have a point

The mean number of 2-torsion elements in the class groups of $n$ -monogenized cubic fields

The proportion of genus one curves over $Q$ defined by a binary quartic that everywhere locally have a point