Let (Formula presented.) be a lacunary sequence of positive real numbers. Rudnick and Technau showed that for almost all (Formula presented.), the pair correlation of (Formula presented.) 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.
Bibliographical noteFunding Information:
SC is supported by the Science and Engineering Research Board, Department of Science and Technology, Government of India under grant SB/S2/RJN‐053/2018. NY is supported by the Israel Science Foundation (grant No. 1881/20).
© 2022 The Authors. Mathematika is copyright © University College London and published by the London Mathematical Society on behalf of University College London.
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