{"title":"黎曼假设的反证","authors":"Igor Hrnčić","doi":"10.13187/rjmr.a.2018.1.19","DOIUrl":null,"url":null,"abstract":"This paper disproves the Riemann hypothesis by generalizing the results about the Perron inversion formula from Titchmarsh's book The Theory of the Riemann Zeta-Function to rearrangements of conditionally convergent series that represent the reciprocal function of zeta. When one replaces the conditionally convergent series in Titchmarsh's theorems and consequent proofs by their rearrangements, the left hand sides of equations change their magnitude, but the right hand sides remain of the same magnitude. This contradiction disproves the Riemann hypothesis.","PeriodicalId":105682,"journal":{"name":"Russian Journal of Mathematical Research. Series A","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Disproof of the Riemann Hypothesis\",\"authors\":\"Igor Hrnčić\",\"doi\":\"10.13187/rjmr.a.2018.1.19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper disproves the Riemann hypothesis by generalizing the results about the Perron inversion formula from Titchmarsh's book The Theory of the Riemann Zeta-Function to rearrangements of conditionally convergent series that represent the reciprocal function of zeta. When one replaces the conditionally convergent series in Titchmarsh's theorems and consequent proofs by their rearrangements, the left hand sides of equations change their magnitude, but the right hand sides remain of the same magnitude. This contradiction disproves the Riemann hypothesis.\",\"PeriodicalId\":105682,\"journal\":{\"name\":\"Russian Journal of Mathematical Research. Series A\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Research. Series A\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13187/rjmr.a.2018.1.19\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Research. Series A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13187/rjmr.a.2018.1.19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper disproves the Riemann hypothesis by generalizing the results about the Perron inversion formula from Titchmarsh's book The Theory of the Riemann Zeta-Function to rearrangements of conditionally convergent series that represent the reciprocal function of zeta. When one replaces the conditionally convergent series in Titchmarsh's theorems and consequent proofs by their rearrangements, the left hand sides of equations change their magnitude, but the right hand sides remain of the same magnitude. This contradiction disproves the Riemann hypothesis.