Arch. Math. (Basel) 108 (2017), 453-463; arXiv:1603.06357v2
Mathematics Subject Classification (2000): 11F11, 11F20, 14C05, 14G15, 14N10
Abstract. We compute the Fourier coefficients of the weight one modular form η(z)η(2z)η(3z)/η(6z) in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates of the modular form η(z)4/η(2z)2. We also explain how to obtain an elementary proof of an identity by Victor Kac. This complements the paper "Complete determination of the zeta function of the Hilbert scheme of n points on a two-dimensional torus" by the same authors.
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(12 octobre 2017)