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On the vanishing of the coefficients of CM eta quotients
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 4 / November 2023
- Published online by Cambridge University Press:
- 18 October 2023, pp. 1202-1216
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- Article
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This work characterizes the vanishing of the Fourier coefficients of all CM (Complex Multiplication) eta quotients. As consequences, we recover Serre’s characterization about that of
$\eta(12z)^{2}$ and recent results of Chang on the pth coefficients of 
$\eta(4z)^{6}$ and 
$\eta(6z)^{4}$. Moreover, we generalize the results on the cases of weight 1 to the setting of binary quadratic forms.
