Van Der Corput序列的差异结果

Uniform distribution theory Pub Date : 2017-10-04 DOI:10.2478/udt-2018-0010

Lukas Spiegelhofer

{"title":"Van Der Corput序列的差异结果","authors":"Lukas Spiegelhofer","doi":"10.2478/udt-2018-0010","DOIUrl":null,"url":null,"abstract":"Abstract Let dN = NDN (ω) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices N such that dN ≤ log N/100. Moreover, we show that the summatory function of dN satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that dN is invariant under digit reversal in base 2.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"26 1","pages":"57 - 69"},"PeriodicalIF":0.0000,"publicationDate":"2017-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Discrepancy Results for The Van Der Corput Sequence\",\"authors\":\"Lukas Spiegelhofer\",\"doi\":\"10.2478/udt-2018-0010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let dN = NDN (ω) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices N such that dN ≤ log N/100. Moreover, we show that the summatory function of dN satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that dN is invariant under digit reversal in base 2.\",\"PeriodicalId\":23390,\"journal\":{\"name\":\"Uniform distribution theory\",\"volume\":\"26 1\",\"pages\":\"57 - 69\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-10-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Uniform distribution theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/udt-2018-0010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Uniform distribution theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/udt-2018-0010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 5

摘要

设dN = NDN (ω)为以2为基数的van der Corput序列的差值。我们改进了已知的N个指标个数的界限，使得dN≤log N/100。此外，我们还证明了dN的求和函数满足一个包含1周期连续函数的精确公式。最后，我们给出了一个新的证明，证明了dN在以2为基数的数字反转下是不变的。

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

Discrepancy Results for The Van Der Corput Sequence

Abstract Let dN = NDN (ω) be the discrepancy of the van der Corput sequence in base 2. We improve on the known bounds for the number of indices N such that dN ≤ log N/100. Moreover, we show that the summatory function of dN satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that dN is invariant under digit reversal in base 2.

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

Uniform distribution theory

自引率

0.00%

发文量