{"title":"On finite pseudorandom binary sequences: functions from a Hardy field","authors":"M. G. Madritsch, J. Rivat, R. F. Tichy","doi":"10.1007/s10474-024-01469-0","DOIUrl":null,"url":null,"abstract":"<div><p>We provide a construction of binary pseudorandom sequences\nbased on Hardy fields <span>\\(\\mathcal{H}\\)</span> as considered by Boshernitzan. In particular we give upper\nbounds for the well distribution measure and the correlation measure defined\nby Mauduit and Sárközy. Finally we show that the correlation measure of order <i>s</i>\nis small only if <i>s</i> is small compared to the “growth exponent” of <span>\\(\\mathcal{H}\\)</span>.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"121 - 137"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01469-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We provide a construction of binary pseudorandom sequences
based on Hardy fields \(\mathcal{H}\) as considered by Boshernitzan. In particular we give upper
bounds for the well distribution measure and the correlation measure defined
by Mauduit and Sárközy. Finally we show that the correlation measure of order s
is small only if s is small compared to the “growth exponent” of \(\mathcal{H}\).
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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