Sums of triangular numbers from the Frobenius determinant |
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Authors: | Hjalmar Rosengren |
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Affiliation: | Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden |
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Abstract: | 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 4m2/d triangles, whenever d|2m, and 4m(m+1)/d triangles, when d|2m or d|2m+2. This extends recent results of Getz and Mahlburg, Milne, and Zagier. |
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Keywords: | primary, 11E25 secondary, 17B65 |
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