Mertens函数的边界

Q4 Mathematics

Advances in Dynamical Systems and Applications Pub Date : 2021-06-30 DOI:10.37622/adsa/16.1.2021.35-44

Darrell Cox, Sourangshu Ghosh, E. Sultanow

{"title":"Mertens函数的边界","authors":"Darrell Cox, Sourangshu Ghosh, E. Sultanow","doi":"10.37622/adsa/16.1.2021.35-44","DOIUrl":null,"url":null,"abstract":"In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(x!) > |M(x)| when x > 1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.","PeriodicalId":36469,"journal":{"name":"Advances in Dynamical Systems and Applications","volume":"22 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Bounds of the Mertens Functions\",\"authors\":\"Darrell Cox, Sourangshu Ghosh, E. Sultanow\",\"doi\":\"10.37622/adsa/16.1.2021.35-44\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(x!) > |M(x)| when x > 1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.\",\"PeriodicalId\":36469,\"journal\":{\"name\":\"Advances in Dynamical Systems and Applications\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Dynamical Systems and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37622/adsa/16.1.2021.35-44\",\"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":"Advances in Dynamical Systems and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37622/adsa/16.1.2021.35-44","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: 3

摘要

本文导出了Mertens函数的一些新性质，并讨论了当x > 1时，Mertens函数绝对值的可能上界√log(x!) > |M(x)|。利用这个似然界，我们证明了我们有一个证明黎曼假设的充分条件。

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

Bounds of the Mertens Functions

In this paper we derive new properties of Mertens function and discuss about a likely upper bound of the absolute value of the Mertens function √log(x!) > |M(x)| when x > 1. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.

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

Advances in Dynamical Systems and Applications Mathematics-Analysis

CiteScore

0.30

自引率

0.00%

发文量