{"title":"关于除数函数的几个猜想","authors":"Masatoshi Nakano","doi":"10.17265/2159-5291/2020.02.002","DOIUrl":null,"url":null,"abstract":": We propose the following conjecture on ( ) n σ the sum-of-divisors function: log( n σ− will increase strictly and converge to 1 when n runs from the colossally abundant numbers to infinity. This conjecture is a sufficient condition for the Riemann hypothesis by Robin’s theorem, and it is confirmed for n from 4 10 up to 103078 10 . Further, we present two additional conjectures that are related to Robin’s theorem.","PeriodicalId":61124,"journal":{"name":"数学和系统科学:英文版","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Conjectures on the Divisor Function\",\"authors\":\"Masatoshi Nakano\",\"doi\":\"10.17265/2159-5291/2020.02.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": We propose the following conjecture on ( ) n σ the sum-of-divisors function: log( n σ− will increase strictly and converge to 1 when n runs from the colossally abundant numbers to infinity. This conjecture is a sufficient condition for the Riemann hypothesis by Robin’s theorem, and it is confirmed for n from 4 10 up to 103078 10 . Further, we present two additional conjectures that are related to Robin’s theorem.\",\"PeriodicalId\":61124,\"journal\":{\"name\":\"数学和系统科学:英文版\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学和系统科学:英文版\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.17265/2159-5291/2020.02.002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学和系统科学:英文版","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.17265/2159-5291/2020.02.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
: We propose the following conjecture on ( ) n σ the sum-of-divisors function: log( n σ− will increase strictly and converge to 1 when n runs from the colossally abundant numbers to infinity. This conjecture is a sufficient condition for the Riemann hypothesis by Robin’s theorem, and it is confirmed for n from 4 10 up to 103078 10 . Further, we present two additional conjectures that are related to Robin’s theorem.
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