Involve, a Journal of Mathematics, Volume 1, Number 1

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

Atanas Atanasov & Rebecca Bellovin & Ivan Loughman-Pawelko & Laura Peskin & Eric Potash

Vol. 1 (2008), No. 1, -

Abstract

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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

Atanas Atanasov
7653 Lerner Hall Columbia University New York, NY 10027 United States

Rebecca Bellovin
1603 Lerner Hall Columbia University New York, NY 10027 United States

Ivan Loughman-Pawelko
4067 Lerner Hall Columbia University New York, NY 10027 United States

Laura Peskin
5991 Lerner Hall Columbia University New York, NY 10027 United States

Eric Potash
4926 Lerner Hall Columbia University New York, NY 10027 United States

Vol. 1, No. 1, 2008

Atanas Atanasov & Rebecca Bellovin & Ivan Loughman-Pawelko & Laura Peskin & Eric Potash

Abstract

Keywords

Mathematical Subject Classification

Authors