Correlations of the Fractional Parts of $\alpha n^{\theta }$

Christopher Lutsko, Niclas Technau

Let $m\ge 3$, we prove that $(\alpha n^{\theta }\mathrm{mod}1{)}_{n>0}$ has Poissonian $m$-point correlation for all $\alpha >0$, provided $\theta <{\theta }_m$, where ${\theta }_m$ is an explicit bound which goes to $0$ as $m$ in…