The distribution of spacings of real‐valued lacunary sequences modulo one

@article{Chaubey2021TheDO,
  title={The distribution of spacings of real‐valued lacunary sequences modulo one},
  author={Sneha Chaubey and Nadav Yesha},
  journal={Mathematika},
  year={2021},
  volume={68}
}
Let (an)n=1∞$(a_{n})_{n=1}^{\infty }$ be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all α∈R$\alpha \in \mathbb {R}$ , the pair correlation of (αan)n=1∞$(\alpha a_{n})_{n=1}^{\infty }$ mod 1 is Poissonian. We show that all higher correlations and hence the nearest‐neighbour spacing distribution are Poissonian as well, thereby extending a result of Rudnick and Zaharescu to real‐valued sequences. 

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