On the correlations of nα mod 1

Niclas Technau; Nadav Yesha

doi:10.4171/JEMS/1281

On the correlations of n^α mod 1

Niclas Technau
, Nadav Yesha

Department of Mathematics

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

Abstract

A well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional parts ¹nαºof the sequence (nα)_n≥1 are uniformly distributed in the unit interval whenever α > 0 is not an integer. For sharpening this knowledge to local statistics, the k-level correlation functions of the sequence (¹nαº)_n≥1 are of fundamental importance. We prove that for each k ≥ 2; the k-level correlation function R_k is Poissonian for almost every α > 4k² - 4k - 1.

Original language	English
Pages (from-to)	4123-4154
Number of pages	32
Journal	Journal of the European Mathematical Society
Volume	25
Issue number	10
DOIs	https://doi.org/10.4171/JEMS/1281
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2022 European Mathematical Society Published by EMS Press and licensed under a CC BY 4.0 license.

Keywords

Uniform distribution modulo 1
correlation functions
local statistics

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.4171/JEMS/1281

Cite this

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