|
|||||
|
|
|
|
|
|
|
|
|
Powers of theta
functions
Heng Huat Chan and Shaun Cooper |
|
Vol. 235 (2008), No. 1, 1–14
|
Abstract |
|
The Ramanujan–Mordell Theorem for sums of an even number of squares is extended to other quadratic forms. A number of explicit examples is given. As an application, the value of the convolution sum  is determined, where σ(m) denotes the sum of the divisors of m. |
Keywords
sum of squares, Ramanujan, convolution sum, modular form,
Eisenstein series
|
Mathematical Subject Classification 2000
Primary: 11E25
Secondary: 33E05, 11F11, 05A19
|
Milestones
Received: 6 November 2007
Revised: 7 December 2007
Accepted: 10 December 2007
Published: 1 March 2008
|
Authors |
| Heng Huat Chan | |
| Department of Mathematics National University of Singapore Kent Ridge 119260 Singapore |
|
| Shaun Cooper | |
| Institute of Information and
Mathematical Sciences Massey University – Albany Private Bag 102904, North Shore Mail Centre Auckland New Zealand |
|
|
