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We study the distribution of spacings between the fractional parts of$n^d\alpha$. For $\alpha$ of high enough Diophantine type we prove a necessaryand sufficient condition for $n^d\alpha\mod 1, 1\leq n\leq N,$ to be Poissonianas $N\to \infty$ along a suitable subsequence.

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