The distribution of spacings between the fractional parts of ${\mathbf{n}}^{\mathbf{d}}\mathbf{\alpha }$

Martino Fassina, Sun Kim, Alexandru Zaharescu

We study the distribution of spacings between the fractional parts of $n^d\alpha$. For $\alpha$ of high enough Diophantine type we prove a necessary and sufficient condition for $n^dα\mod 1,…