Involve: A Journal of Mathematics
- Volume 1, Number 1 (2008), 111-121.
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 as the sum of triangular numbers is asymptotically equivalent to the modified divisor function .
Involve, Volume 1, Number 1 (2008), 111-121.
Received: 30 October 2007
Accepted: 19 January 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11F11: Holomorphic modular forms of integral weight
Atanasov, Atanas; Bellovin, Rebecca; Loughman-Pawelko, Ivan; Peskin, Laura; Potash, Eric. An asymptotic for the representation of integers as sums of triangular numbers. Involve 1 (2008), no. 1, 111--121. doi:10.2140/involve.2008.1.111. https://projecteuclid.org/euclid.involve/1513799074