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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 σ2k−1♯(2n + k). |
Keywordsmodular form, triangular number, asymptotics |
Mathematical Subject ClassificationPrimary: 11F11 |
Authors |
| Atanas Atanasov |
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7653 Lerner Hall Columbia University New York, NY 10027 United States |
| Rebecca Bellovin |
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1603 Lerner Hall Columbia University New York, NY 10027 United States |
| Ivan Loughman-Pawelko |
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4067 Lerner Hall Columbia University New York, NY 10027 United States |
| Laura Peskin |
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5991 Lerner Hall Columbia University New York, NY 10027 United States |
| Eric Potash |
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4926 Lerner Hall Columbia University New York, NY 10027 United States |
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