We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $\operatorname{SL}_{3}(\mathbf{Z})$ do not correlate with $q$ -periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky–Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes.

中文翻译：

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自形态的周期性扭曲

我们证明长度之和约为 $q^{3/2}$ 自守形式的 Hecke 特征值 $\operatorname{SL}_{3}(\mathbf{Z})$ 不相关 $q$ - 有界傅里叶变换的周期函数。这概括了 Munshi 和 Holowinsky-Nelson 的早期结果，对应于乘法狄利克雷特征，特别适用于小导体模素数的迹函数。