Sums of triangular numbers from the Frobenius determinant
| dc.creator | Rosengren, Hjalmar | |
| dc.date | 2005-04-13 | |
| dc.date | 2005-05-17 | |
| dc.date.accessioned | 2026-07-07T06:34:22Z | |
| dc.date.available | 2026-07-07T06:34:22Z | |
| dc.description | We show that the denominator formula for the strange series of affine superalgebras, conjectured by Kac and Wakimoto and proved by Zagier, follows from a classical determinant evaluation of Frobenius. As a limit case, we obtain exact formulas for the number of representations of an arbitrary number as a sum of 4m^2/d triangles, whenever d divides 2m, and 4m(m+1)/d triangles, when d divides 2m or d divides 2m+2. This extends recent results of Getz and Mahlburg, Milne, and Zagier. | |
| dc.description | 27 pages; minor changes from previous version | |
| dc.identifier | https://arxiv.org/abs/math/0504272 | |
| dc.identifier | http://arxiv.org/abs/math/0504272 | |
| dc.identifier | Adv. Math. 208 (2007), 935-961 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99507 | |
| dc.subject | Number Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 11E25; 17B65 | |
| dc.title | Sums of triangular numbers from the Frobenius determinant | |
| dc.type | text |