A. Shankar

activity

20102026

most citedThe average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1

45 citations · 246 across the 34 of their papers we have counts for

collaborators

Showing 2017Show all

2 papers · 1 filter

math.NT2017★ 5 cited

The number of quartic $D_{4}$ -fields ordered by conductor

Salim Ali Altug, Arul Shankar, Ila Varma +1

We consider families of number fields of degree 4 whose normal closures over $Q$ have Galois group isomorphic to $D_{4}$ , the symmetries of a square. To any such field $L$ ,…

math.NT2017★ 13 cited

Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves

Manjul Bhargava, Arul Shankar, Takashi Taniguchi +3

We prove the first known nontrivial bounds on the sizes of the 2-torsion subgroups of the class groups of cubic and higher degree number fields $K$ (the trivial bound being $O_ε(|{…

The number of quartic D4​-fields ordered by conductor

Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves

The number of quartic $D_{4}$ -fields ordered by conductor