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Are the Fourier coefficients of $\eta(q^m)^m / \eta(q)$ non-negative?

In this paper, the following result is proved. For any prime $p$, all the Fourier coefficients of $$\eta(q^p)^p / \eta(q) = q^{\frac{p^2-1}{12}} \prod_{n=1}^\infty (1 - q^{pn})^p (1 - q^{n})^{-1}$$ ...
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