Weak generalized Ramanujan conjecture for L-function coefficients

Let $L(f,s)=\sum_{n=1}^{\infty}\lambda_f(n)n^{-s}$ be the self-dual $L$-function considered in the paper, with real coefficients $\lambda_f(n)$.

Weak generalized Ramanujan conjecture. There exists $\eta>0$ such that, for every $n\geqslant 1$,

$$\lambda_f(n) \ll_f n^{\frac{1}{6}-\eta}.$$

This coefficient bound is another conjectural hypothesis used in the paper's study of short coefficient sums. The source gives no resolution status.