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

University of Haifa

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	American 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

Keywords

math.NT

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1112/mtk.12129

https://arxiv.org/abs/2108.00431

Cite this

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title = "The distribution of spacings of real-valued lacunary sequences modulo one",

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.",

keywords = "math.NT",

author = "Sneha Chaubey and Nadav Yesha",

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: {\textcopyright} 2022 The Authors. Mathematika is copyright {\textcopyright} University College London and published by the London Mathematical Society on behalf of University College London.",

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AU - Chaubey, Sneha

AU - Yesha, Nadav

N1 - 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.

PY - 2022/4

Y1 - 2022/4

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.

KW - math.NT

U2 - 10.1112/mtk.12129

DO - 10.1112/mtk.12129

M3 - Article

SN - 0025-5793

VL - 68

SP - 416

EP - 428

JO - Mathematika

JF - Mathematika

IS - 2

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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