[Corrigendum] Note on the Riemann Hypothesis: International Conference on Recent Developments in Mathematics (ICRDM 2022)

15 June 2023, Version 1
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

Robin's criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma} \cdot n \cdot \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$ and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. In this note, using Robin's inequality on superabundant numbers, we prove that the Riemann hypothesis is true. This is a "Corrigendum" for a paper presentation at the ICRDM 2022 held at Canadian University Dubai, Dubai, UAE during 24-26 August 2022. Besides, this proof is an extension of the article "Robin's criterion on divisibility" published by The Ramanujan Journal on May 3rd, 2022.

Keywords

Riemann hypothesis
Prime numbers
Sum-of-divisors function
Robin's inequality
Superabundant numbers

Supplementary materials

Title
Description
Actions
Title
Paper Presentation Certificate
Description
Certificate of presentation at the ICRDM 2022 held at Canadian University Dubai, Dubai, UAE during 24-26 August 2022.
Actions

Supplementary weblinks

Comments

Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting and Discussion Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.