n^{\beta-0}\sum_{x\in\mathbb{Z}} \Biggl|\sum_{i=0}^k\theta_i\hat {\Gamma}_n(\tau_i,\{x/n\}) \Biggr|^\beta\stackrel{\mathcal{D}}{=} n^{\beta-0}\sum_{x\in\mathbb{Z}} \Biggl|\sum_{i=0}^k\theta_i\Gamma _n(\tau_i,\{x/n\}) \Biggr|^\beta