{"title":"A probability estimate for the discrepancy of Korobov lattice points","authors":"A. A. Illarionov","doi":"10.1070/SM9522","DOIUrl":null,"url":null,"abstract":"Bykovskii (2002) obtained the best current upper estimate for the minimum discrepancy of the Korobov lattice points from the uniform distribution. We show that this estimate holds for almost all -dimensional Korobov lattices of nodes, where , and is a prime number. Bibliography: 14 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"27 Suppl 1 1","pages":"1571 - 1587"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9522","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Bykovskii (2002) obtained the best current upper estimate for the minimum discrepancy of the Korobov lattice points from the uniform distribution. We show that this estimate holds for almost all -dimensional Korobov lattices of nodes, where , and is a prime number. Bibliography: 14 titles.
期刊介绍：
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in:
Mathematical analysis
Ordinary differential equations
Partial differential equations
Mathematical physics
Geometry
Algebra
Functional analysis
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