Abstract

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 n as the sum of k triangular numbers is asymptotically equivalent to the modified divisor function σ_2k−1^♯(2n + k).

Keywords

modular form, triangular number, asymptotics

Mathematical Subject Classification

Primary: 11F11

Authors