论有限伪随机二进制序列：来自哈代域的函数

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-10-22 DOI:10.1007/s10474-024-01469-0

M. G. Madritsch, J. Rivat, R. F. Tichy

{"title":"论有限伪随机二进制序列：来自哈代域的函数","authors":"M. G. Madritsch, J. Rivat, R. F. Tichy","doi":"10.1007/s10474-024-01469-0","DOIUrl":null,"url":null,"abstract":"<div>We provide a construction of binary pseudorandom sequences\nbased on Hardy fields \\(\\mathcal{H}\\) 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 s\nis small only if s is small compared to the “growth exponent” of \\(\\mathcal{H}\\).</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":"{\"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>We provide a construction of binary pseudorandom sequences\\nbased on Hardy fields \\\\(\\\\mathcal{H}\\\\) 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 s\\nis small only if s is small compared to the “growth exponent” of \\\\(\\\\mathcal{H}\\\\).</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}","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

摘要

我们提供了一种基于博舍尼赞所考虑的哈代场 \(\mathcal{H}\)的二进制伪随机序列的构造。我们特别给出了莫迪特（Mauduit）和萨尔科齐（Sárközy）定义的井分布度量和相关度量的上限。最后我们证明，只有当s小于\(\mathcal{H}\)的 "增长指数 "时，阶s的相关度量才是小的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On finite pseudorandom binary sequences: functions from a Hardy field

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 \(\mathcal{H}\).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

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.