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Affiliation(s)

Kesennuma College of Technology, 1-174 Ohtougeyama Kesennuma-shi, Miyagi 988-0812, Japan

ABSTRACT

We propose the following conjecture onthe sum-of-divisors function:will increase strictly and converge to when n runs from the colossally abundant numbers to infinity This conjecture is a sufficient condition for the and converge to whenruns 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 up to 10103078. Further, we present two additional Riemann hypothesis by Robin’s theorem, and it is confirmed for from up to 10103078. Further, we present two additional conjectures that are related to Robin’s theorem.

KEYWORDS

Riemann hypothesis, Robin’s theorem, colossally abundant number, divisor function.

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