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arXiv · 1603.06357

The Fourier expansion of \eta(z)\eta(2z)\eta(3z)/\eta(6z)

Christian Kassel·Christophe Reutenauer
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Abstract

We compute the Fourier coefficients of the weight one modular form $\eta(z)\eta(2z)\eta(3z)/\eta(6z)$ 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 $\eta(z)^4/\eta(2z)^2$. In the last section we use our main result to give an elementary proof of an identity by Victor Kac.

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Christian Kassel, Christophe Reutenauer. 2016-03-21. The Fourier expansion of \eta(z)\eta(2z)\eta(3z)/\eta(6z). https://doi.org/10.1007/s00013-017-1033-4

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