<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>8644</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>422</pageFirst>
    <pageLast>437</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>259</volume>
    <type>article</type>
    <publisherName>Elsevier</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms</title>
    <abstract language="eng">In any dimension d ≥ 2, there is no known example of a low-discrepancy sequence which possesses Poisssonian&#13;
pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β-Poissonian pair correlations for all 0 &lt; β &lt; 1 d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β = 1 d ). In this paper, we further elaborate on the closeness of the two notions. We show that d-dimensional Kronecker sequences for badly approximable vectors � α with an arbitrary small uniformly distributed stochastic error term generically have β = 1 d -Poissonian pair correlations.</abstract>
    <parentTitle language="eng">Journal of Number Theory</parentTitle>
    <identifier type="issn">0022-314X</identifier>
    <identifier type="doi">10.1016/j.jnt.2023.12.011</identifier>
    <enrichment key="opus_doi_flag">true</enrichment>
    <enrichment key="opus_import_data">{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T11:35:49Z","timestamp":1763811349630,"version":"3.44.0"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Number Theory"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1016\/j.jnt.2023.12.011","type":"journal-article","created":{"date-parts":[[2024,2,20]],"date-time":"2024-02-20T16:12:23Z","timestamp":1708445543000},"page":"422-437","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms"],"prefix":"10.1016","volume":"259","author":[{"given":"Anja","family":"Schmiedt","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3866-6874","authenticated-orcid":false,"given":"Christian","family":"Wei\u00df","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jnt.2023.12.011_br0010","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.jnt.2017.06.009","article-title":"Pair correlations and equidistribution","volume":"182","author":"Aistleitner","year":"2018","journal-title":"J. Number Theory"},{"key":"10.1016\/j.jnt.2023.12.011_br0020","doi-asserted-by":"crossref","first-page":"1573","DOI":"10.1007\/s00209-021-02939-9","article-title":"On badly approximabel vectors","volume":"301","author":"Akhunzhanov","year":"2022","journal-title":"Math. Z."},{"issue":"3","key":"10.1016\/j.jnt.2023.12.011_br0030","first-page":"269","article-title":"A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution","volume":"72","author":"Beck","year":"1989","journal-title":"Compos. Math."},{"issue":"2","key":"10.1016\/j.jnt.2023.12.011_br0040","doi-asserted-by":"crossref","first-page":"449","DOI":"10.2307\/2118607","article-title":"Probabilistic Diophantine approximation, I. Kronecker sequences","volume":"140","author":"Beck","year":"1994","journal-title":"Ann. Math."},{"issue":"9","key":"10.1016\/j.jnt.2023.12.011_br0050","doi-asserted-by":"crossref","first-page":"2470","DOI":"10.1016\/j.jfa.2007.09.010","article-title":"On the small ball inequality in all dimensions","volume":"254","author":"Bilyk","year":"2008","journal-title":"J. Funct. Anal."},{"key":"10.1016\/j.jnt.2023.12.011_br0060","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1007\/s10231-011-0208-z","article-title":"Discrepancy of LS-sequences of partitions and points","volume":"191","author":"Carbone","year":"2012","journal-title":"Ann. Mat. Pura Appl."},{"issue":"7","key":"10.1016\/j.jnt.2023.12.011_br0070","doi-asserted-by":"crossref","first-page":"2815","DOI":"10.1090\/S0002-9939-2015-12489-6","article-title":"The two-point correlation function of the fractional parts of n is Poisson","volume":"143","author":"El-Baz","year":"2015","journal-title":"Proc. Am. Math. Soc."},{"key":"10.1016\/j.jnt.2023.12.011_br0080","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s00013-017-1060-1","article-title":"On pair correlation and discrepancy","volume":"109","author":"Grepstad","year":"2017","journal-title":"Arch. Math."},{"key":"10.1016\/j.jnt.2023.12.011_br0090","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/s00605-019-01267-9","article-title":"On a multi-dimensional Poissonian pair correlation concept and uniform distribution","volume":"190","author":"Hinrichs","year":"2019","journal-title":"Monatshefte Math."},{"author":"Hauke","key":"10.1016\/j.jnt.2023.12.011_br0100"},{"year":"1974","series-title":"Uniform Distribution of Sequences","author":"Kuipers","key":"10.1016\/j.jnt.2023.12.011_br0110"},{"author":"Lachmann","key":"10.1016\/j.jnt.2023.12.011_br0120"},{"issue":"2","key":"10.1016\/j.jnt.2023.12.011_br0130","doi-asserted-by":"crossref","DOI":"10.1016\/j.disc.2019.111656","article-title":"Some negative results related to Poissonian pair correlation problems","volume":"343","author":"Larcher","year":"2020","journal-title":"Discrete Math."},{"author":"Lutsko","key":"10.1016\/j.jnt.2023.12.011_br0140"},{"key":"10.1016\/j.jnt.2023.12.011_br0150","series-title":"Equidistribution in Number Theory, an Introduction","article-title":"Distribution modulo one and Ratner's theorem","volume":"vol. 237","author":"Marklof","year":"2007"},{"key":"10.1016\/j.jnt.2023.12.011_br0160","article-title":"Random Number Generation and Quasi-Monte Carlo Methods","volume":"vol. 63","author":"Niederreiter","year":"1992"},{"key":"10.1016\/j.jnt.2023.12.011_br0170","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s11856-006-0009-z","article-title":"Pair correlations of sequences in higher dimensions","volume":"157","author":"Nair","year":"2007","journal-title":"Isr. J. Math."},{"key":"10.1016\/j.jnt.2023.12.011_br0180","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1112\/S0025579300000541","article-title":"On irregularities of distribution","volume":"1","author":"Roth","year":"1954","journal-title":"Mathematika"},{"key":"10.1016\/j.jnt.2023.12.011_br0190","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s002200050348","article-title":"The pair correlation function of fractional parts of polynomials","volume":"194","author":"Rudnick","year":"1998","journal-title":"Commun. Math. Phys."},{"key":"10.1016\/j.jnt.2023.12.011_br0200","doi-asserted-by":"crossref","first-page":"45","DOI":"10.4064\/aa-21-1-45-50","article-title":"Irregularities of distribution vii","volume":"21","author":"Schmidt","year":"1972","journal-title":"Acta Arith."},{"key":"10.1016\/j.jnt.2023.12.011_br0210","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jnt.2019.07.011","article-title":"Poissonian pair correlation in higher dimension","volume":"208","author":"Steinerberger","year":"2020","journal-title":"J. Number Theory"},{"key":"10.1016\/j.jnt.2023.12.011_br0220","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s10231-018-0782-4","article-title":"Interval exchange transformations and low-discrepancy","volume":"198","author":"Wei\u00df","year":"2019","journal-title":"Ann. Mat. Pura Appl."},{"key":"10.1016\/j.jnt.2023.12.011_br0230","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1007\/s00605-022-01742-w","article-title":"Some connections between discrepancy, finite gap properties and pair correlations","volume":"199","author":"Wei\u00df","year":"2022","journal-title":"Monatshefte Math."},{"key":"10.1016\/j.jnt.2023.12.011_br0240","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1007\/BF01475864","article-title":"Ueber die Gleichverteilung von Zahlen mod. Eins","volume":"3","author":"Weyl","year":"1916","journal-title":"Math. Ann."},{"key":"10.1016\/j.jnt.2023.12.011_br0250","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.jnt.2021.07.011","article-title":"Sequences with almost Poissonian pair correlations","volume":"236","author":"Wei\u00df","year":"2022","journal-title":"J. Number Theory"}],"container-title":["Journal of Number Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022314X24000295?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0022314X24000295?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T05:40:35Z","timestamp":1758346835000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0022314X24000295"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6]]},"references-count":25,"alternative-id":["S0022314X24000295"],"URL":"https:\/\/doi.org\/10.1016\/j.jnt.2023.12.011","relation":{},"ISSN":["0022-314X"],"issn-type":[{"type":"print","value":"0022-314X"}],"subject":[],"published":{"date-parts":[[2024,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms","name":"articletitle","label":"Article Title"},{"value":"Journal of Number Theory","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jnt.2023.12.011","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2024 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}</enrichment>
    <enrichment key="local_crossrefDocumentType">journal-article</enrichment>
    <enrichment key="local_crossrefLicence">https://www.elsevier.com/tdm/userlicense/1.0/</enrichment>
    <enrichment key="local_import_origin">crossref</enrichment>
    <enrichment key="local_doiImportPopulated">PersonAuthorFirstName_1,PersonAuthorLastName_1,PersonAuthorFirstName_2,PersonAuthorLastName_2,PersonAuthorIdentifierOrcid_2,PublisherName,TitleMain_1,Language,TitleParent_1,PageNumber,PageFirst,PageLast,Volume,CompletedYear,IdentifierIssn,Enrichmentlocal_crossrefLicence</enrichment>
    <enrichment key="BegutachtungStatus">peer-reviewed</enrichment>
    <enrichment key="opus.source">doi-import</enrichment>
    <licence>Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG</licence>
    <author>Anja Schmiedt</author>
    <author>Christian Weiß</author>
    <collection role="institutes" number="FakIM">Fakultät Informatik und Mathematik</collection>
    <collection role="DFGFachsystematik" number="4">Naturwissenschaften</collection>
    <collection role="othforschungsschwerpunkt" number="">Digitale Transformation</collection>
  </doc>
</export-example>
