Correlation of fractional parts of n2α

Alexandriu Zaharescu

doi:10.1515/form.2003.004

Correlation of fractional parts of n²α

Alexandriu Zaharescu

Mathematics

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

Abstract

We study the correlation measures associated to sequences of the form n²α (mod 1). For well approximate irrational numbers α we show that a necessary and sufficient condition for n²α (mod 1) to have Poissonian subsequences is that the denominators of good approximants to α are essentially square free.

Original language	English (US)
Pages (from-to)	1-21
Number of pages	21
Journal	Forum Mathematicum
Volume	15
Issue number	1
DOIs	https://doi.org/10.1515/form.2003.004
State	Published - 2003

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Online availability

10.1515/form.2003.004

Library availability

Discover UIUC Full Text

Cite this

@article{037788c1b79941b1b70bcf10b42b4061,

title = "Correlation of fractional parts of n2α",

abstract = "We study the correlation measures associated to sequences of the form n2α (mod 1). For well approximate irrational numbers α we show that a necessary and sufficient condition for n2α (mod 1) to have Poissonian subsequences is that the denominators of good approximants to α are essentially square free.",

author = "Alexandriu Zaharescu",

year = "2003",

doi = "10.1515/form.2003.004",

language = "English (US)",

volume = "15",

pages = "1--21",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Correlation of fractional parts of n2α

AU - Zaharescu, Alexandriu

PY - 2003

Y1 - 2003

N2 - We study the correlation measures associated to sequences of the form n2α (mod 1). For well approximate irrational numbers α we show that a necessary and sufficient condition for n2α (mod 1) to have Poissonian subsequences is that the denominators of good approximants to α are essentially square free.

AB - We study the correlation measures associated to sequences of the form n2α (mod 1). For well approximate irrational numbers α we show that a necessary and sufficient condition for n2α (mod 1) to have Poissonian subsequences is that the denominators of good approximants to α are essentially square free.

UR - http://www.scopus.com/inward/record.url?scp=0042671470&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042671470&partnerID=8YFLogxK

U2 - 10.1515/form.2003.004

DO - 10.1515/form.2003.004

M3 - Article

AN - SCOPUS:0042671470

SN - 0933-7741

VL - 15

SP - 1

EP - 21

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 1

ER -