Liouville λ函数的两种推广

IF 0.4 Q4 MATHEMATICS

Notes on Number Theory and Discrete Mathematics Pub Date : 2023-02-13 DOI:10.7546/nntdm.2023.29.1.30-39

A. P. Camargo

{"title":"Liouville λ函数的两种推广","authors":"A. P. Camargo","doi":"10.7546/nntdm.2023.29.1.30-39","DOIUrl":null,"url":null,"abstract":"We study the properties of two classes of functions $\\lambda_k$ and $\\tilde{\\lambda}_k$ that generalize the Liouville $\\lambda$ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of $\\lambda_k$ and $\\tilde{\\lambda}_k.$ Similar results are obtained for the generalization of the Möbius function considered by Tanaka.","PeriodicalId":44060,"journal":{"name":"Notes on Number Theory and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two generalizations of Liouville λ function\",\"authors\":\"A. P. Camargo\",\"doi\":\"10.7546/nntdm.2023.29.1.30-39\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the properties of two classes of functions $\\\\lambda_k$ and $\\\\tilde{\\\\lambda}_k$ that generalize the Liouville $\\\\lambda$ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of $\\\\lambda_k$ and $\\\\tilde{\\\\lambda}_k.$ Similar results are obtained for the generalization of the Möbius function considered by Tanaka.\",\"PeriodicalId\":44060,\"journal\":{\"name\":\"Notes on Number Theory and Discrete Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-02-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notes on Number Theory and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/nntdm.2023.29.1.30-39\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notes on Number Theory and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/nntdm.2023.29.1.30-39","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了推广Liouville$\lambda函数的两类函数$\lambda_k$和$\tilde｛\lambda｝_k$的性质，包括Riemann假设和关于$\lambda_k$与$\tilder｛\lLambda｝_ k的求和函数渐近性态的一些断言之间的一些等价性Tanaka所考虑的Möbius函数的推广也得到了类似的结果。

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

Two generalizations of Liouville λ function

We study the properties of two classes of functions $\lambda_k$ and $\tilde{\lambda}_k$ that generalize the Liouville $\lambda$ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of $\lambda_k$ and $\tilde{\lambda}_k.$ Similar results are obtained for the generalization of the Möbius function considered by Tanaka.

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

Notes on Number Theory and Discrete Mathematics MATHEMATICS-

自引率

33.30%

发文量