On sums involving coefficients of automorphic $L$-functions

Let $L(s,\pi)$ be the automorphic $L$-function associated to an automorphic irreducible cuspidal representation $\pi$ of GL$_m$ over $\mathbb{Q}$, and let $a_{\pi}(n)$ be the $n$th coefficient in its Dirichlet series expansion. In this paper we prove that if at every finite place $p$, $\pi_p$ is unramified, then for any $\varepsilon>0$,

$A_{\pi}(x)=\sum_{n \leq x}a_{\pi}(n) \ll_{\varepsilon,\pi} \left\... ... x^{\frac{m^2-m}{m^2+1}+\varepsilon}& \text{ if }& m \geq 3. \end{array}\right.$