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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 and Eric Potash
Vol. 1 (2008), No. 1, 111–121
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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 as the sum of triangular numbers is asymptotically equivalent to the modified divisor function . |
Keywords
modular form, triangular number, asymptotics
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Mathematical Subject Classification 2000
Primary: 11F11
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Milestones
Received: 30 October 2007
Accepted: 19 January 2008
Published: 28 February 2008
Communicated by Ken Ono
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Authors |
| Atanas Atanasov | |
| 7653 Lerner Hall Columbia University New York, NY 10027 United States |
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| Rebecca Bellovin | |
| 1603 Lerner Hall Columbia University New York, NY 10027 United States |
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| Ivan Loughman-Pawelko | |
| 4067 Lerner Hall Columbia University New York, NY 10027 United States |
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| Laura Peskin | |
| 5991 Lerner Hall Columbia University New York, NY 10027 United States |
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| Eric Potash | |
| 4926 Lerner Hall Columbia University New York, NY 10027 United States |
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