Arul Shankar

Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

On the Davenport–Heilbronn theorems and second order terms

Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

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

The average number of elements in the 4-Selmer groups of elliptic curves is 7

COUNTING -FIELDS WITH A POWER SAVING ERROR TERM

Squarefree values of polynomial discriminants I

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

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

AVERAGE RANK OF ELLIPTIC CURVES