关于CM - Eta商系数的消失性

Pub Date : 2023-10-18 DOI:10.1017/s0013091523000627

Tim Huber, Chang Liu, James McLaughlin, Dongxi Ye, Miaodan Yuan, Sumeng Zhang

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引用次数: 0

摘要

摘要本文刻画了所有CM(复数乘法)的eta商的傅里叶系数的消失。作为结果，我们恢复了Serre关于$\eta(12z)^{2}$的表征以及Chang关于$\eta(4z)^{6}$和$\eta(6z)^{4}$的系数p的最新结果。此外，我们将权值为1的情况下的结果推广到二元二次型的设置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Vanishing of the Coefficients of CM Eta Quotients

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 p th 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.

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