On the vanishing of the coefficients of CM eta quotients

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow
Chang Liu
James McLaughlin
Dongxi Ye
Miaodan Yuan
Sumeng Zhang

Document Type

Article

Publication Date

10-18-2023

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 η(12z)2 and recent results of Chang on the pth coefficients of η(4z)6 and η(6z)4 . Moreover, we generalize the results on the cases of weight 1 to the setting of binary quadratic forms.

Comments

© The Author(s), 2023. Original published version available at https://doi.org/10.1017/S0013091523000627

Recommended Citation

Huber, Tim, Chang Liu, James McLaughlin, Dongxi Ye, Miaodan Yuan, and Sumeng Zhang. "On the vanishing of the coefficients of CM eta quotients." Proceedings of the Edinburgh Mathematical Society 66, no. 4 (2023): 1202-1216. https://doi.org/10.1017/S0013091523000627

Publication Title

Proceedings of the Edinburgh Mathematical Society

DOI

10.1017/S0013091523000627