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On the vanishing of the coefficients of CM eta quotients
Published online by Cambridge University Press: 18 October 2023
Abstract
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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 4 , November 2023 , pp. 1202 - 1216
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
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