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2008 An asymptotic for the representation of integers as sums of triangular numbers
Atanas Atanasov, Rebecca Bellovin, Ivan Loughman-Pawelko, Laura Peskin, Eric Potash
Involve 1(1): 111-121 (2008). DOI: 10.2140/involve.2008.1.111

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 σ2k1(2n+k).

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Atanas Atanasov. Rebecca Bellovin. Ivan Loughman-Pawelko. Laura Peskin. Eric Potash. "An asymptotic for the representation of integers as sums of triangular numbers." Involve 1 (1) 111 - 121, 2008. https://doi.org/10.2140/involve.2008.1.111

Information

Received: 30 October 2007; Accepted: 19 January 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1229.11066
MathSciNet: MR2403070
Digital Object Identifier: 10.2140/involve.2008.1.111

Subjects:
Primary: 11F11

Keywords: asymptotics , modular form , triangular number

Rights: Copyright © 2008 Mathematical Sciences Publishers

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