\] For $ \tau_0,\ldots,\tau_k\geq0 $ and $ \theta_0,\ldots,\theta _k\in\mathbb{R} $, the two sequences of random variables $$\begin{aligned} &&n^{-0-{\beta/\alpha}}\sum_{x\in\mathbb{Z}} \Biggl|\sum _{i=0}^k\theta_i\Gamma(k_n\tau_i,\{x\}) \Biggr|^\beta