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

Christopher Lutsko, Athanasios Sourmelidis, Niclas Technau

Fix $\alpha ,\theta >0$, and consider the sequence $(\alpha n^{\theta }\mathrm{mod}1{)}_{n\ge 1}$. Since the seminal work of Rudnick--Sarnak (1998), and due to the Berry--Tabor conjecture in quantum chaos, the fine…