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

Let $\{x_i\}:=\{x_1=5, x_2=13, x_3=29, x_4=37, x_5=45, \dots \}$ be the sequence of those positive integers of the form $$ p^{4\alpha+1}n^2$$ in increasing order where $p\equiv 5\pmod 8$ is prime ...