Some Conjectures on the Divisor Function  

作　　者：Masatoshi Nakano 

机构地区：[1]Kesennuma College of Technology,1-174 Ohtougeyama Kesennuma-shi,Miyagi 988-0812,Japan

出　　处：《Journal of Mathematics and System Science》2020年第2期13-22,共10页数学和系统科学（英文版）

摘　　要：We propose the following conjecture on(σ)n the sum-of-divisors function:log(e'nlog logn-σ(n))/log(e'nlog log n)will increase strictly and converge to1 when n runs from the colossally abundant numbers to infinity This conjecture is a sufficient condition for the and converge to1 when n nuns from the colossally abundant numbers to infinity.This conjecture is a sufficient condition for the Ricemann hypothesis by Robin's theorem,and it is confirmed for n from10^(4 )up to 10^(103078) Further,we present two additional Riemann hypothesis by Robin's theorem,and it is confirmed forn from 10^(4) up to 10^(103078) Further,we present two additional conjectures that are related to Robin's theorem.

关 键 词：Riemann hypothesis Robin’s theorem colossally abundant number divisor function. 

分 类 号：O17[理学—数学]