Sums of Triangular Numbers from the Frobenius Determinant
نویسنده
چکیده
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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