An asymptotic for the representation of integers as sums of triangular numbers

Motivated by the result of Rankin for representations of integers as sums of squares, we use a decomposition of a modular form into a particular Eisenstein series and a cusp form to show that the number of ways of representing a positive integer [math] as the sum of [math] triangular numbers is asymptotically equivalent to the modified divisor function [math] .