类对数函数与模1的均匀分布

Uniform distribution theory Pub Date : 2018-12-01 DOI:10.2478/udt-2018-0013

M. Rehberg

{"title":"类对数函数与模1的均匀分布","authors":"M. Rehberg","doi":"10.2478/udt-2018-0013","DOIUrl":null,"url":null,"abstract":"Abstract For a function f satisfying f (x) = o((log x) K), K > 0, and a sequence of numbers (qn) n, we prove by assuming several conditions on f that the sequence (αf (qn)) n≥n0 is uniformly distributed modulo one for any nonzero real number α. This generalises some former results due to Too, Goto and Kano where instead of (qn) n the sequence of primes was considered.","PeriodicalId":23390,"journal":{"name":"Uniform distribution theory","volume":"102 1","pages":"101 - 93"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Log-Like Functions and Uniform Distribution Modulo One\",\"authors\":\"M. Rehberg\",\"doi\":\"10.2478/udt-2018-0013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract For a function f satisfying f (x) = o((log x) K), K > 0, and a sequence of numbers (qn) n, we prove by assuming several conditions on f that the sequence (αf (qn)) n≥n0 is uniformly distributed modulo one for any nonzero real number α. This generalises some former results due to Too, Goto and Kano where instead of (qn) n the sequence of primes was considered.\",\"PeriodicalId\":23390,\"journal\":{\"name\":\"Uniform distribution theory\",\"volume\":\"102 1\",\"pages\":\"101 - 93\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Uniform distribution theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/udt-2018-0013\",\"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-2018-0013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

摘要对于满足f (x) = o((log x) K)， K > 0和数列(qn) n的函数f，通过在f上假设几个条件，证明了数列(αf (qn)) n≥n0对于任意非零实数α是均匀分布模1。这推广了由于Too, Goto和Kano的一些先前的结果，其中考虑的不是素数序列中的(qn)。

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

Log-Like Functions and Uniform Distribution Modulo One

Abstract For a function f satisfying f (x) = o((log x) K), K > 0, and a sequence of numbers (qn) n, we prove by assuming several conditions on f that the sequence (αf (qn)) n≥n0 is uniformly distributed modulo one for any nonzero real number α. This generalises some former results due to Too, Goto and Kano where instead of (qn) n the sequence of primes was considered.

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