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

Sneha Chaubey; Nadav Yesha

doi:10.1112/mtk.12129

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

Sneha Chaubey, Nadav Yesha

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	416-428
Number of pages	13
Journal	Mathematika
Volume	68
Issue number	2
DOIs	https://doi.org/10.1112/mtk.12129
State	Published - Apr 2022

Bibliographical note

Funding 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).

Publisher Copyright:
© 2022 The Authors. Mathematika is copyright © University College London and published by the London Mathematical Society on behalf of University College London.

Keywords

math.NT

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1112/mtk.12129

https://arxiv.org/abs/2108.00431

Cite this

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N2 - 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.

AB - 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.

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this