On $\mathrm{G}{\mathrm{L}}_3$ Fourier coefficients over values of mixed powers

Qingfeng Sun, Yanxue Yu

Let $A_{\ddot{I}}€(n,1)$ be the $(n,1)$-th Fourier coefficient of the Hecke-Maass cusp form $\ddot{I}€$ for $\mathrm{S}{\mathrm{L}}_3(\mathbb{Z})$ and $\ddot{I}‰(x)$ be a smooth compactly supported function. In this pa…