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 2016 · math.NTShow all

3 papers · 2 filters

math.NT2016★ 44 cited

Squarefree values of polynomial discriminants I

Manjul Bhargava, Arul Shankar, Xiaoheng Wang

We determine the density of monic integer polynomials of given degree $n > 1$ that have squarefree discriminant; in particular, we prove for the first time that the lower density of…

math.NT2016★ 23 cited

The average size of the 3-isogeny Selmer groups of elliptic curves $y^{2} = x^{3} + k$

Manjul Bhargava, Noam Elkies, Ari Shnidman

The elliptic curve $E_{k} : y^{2} = x^{3} + k$ admits a natural 3-isogeny $ϕ_{k} : E_{k} \to E_{- 27 k}$ . We compute the average size of the $ϕ_{k}$ -Selmer group as $k$ varies over the…

math.NT2016★ 10 cited

A positive proportion of Thue equations fail the integral Hasse principle

Shabnam Akhtari, Manjul Bhargava

For any nonzero $h \in Z$ , we prove that a positive proportion of integral binary cubic forms $F$ do locally everywhere represent $h$ but do not globally represent $h$ ; that…

Squarefree values of polynomial discriminants I

The average size of the 3-isogeny Selmer groups of elliptic curves y2=x3+k

A positive proportion of Thue equations fail the integral Hasse principle

The average size of the 3-isogeny Selmer groups of elliptic curves $y^{2} = x^{3} + k$