The distribution of spacings of real-valued lacunary sequences modulo one
Abstract
Let (an)n=1∞ be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all α∈R, the pair correlation of (α an)n=1∞ 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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