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

EasyChair Preprint 10373

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.

Keyphrases: Riemann hypothesis, Robin's inequality, Superabundant numbers, prime numbers, sum-of-divisors function

@booklet{EasyChair:10373,
  author    = {Frank Vega},
  title     = {[Corrigendum] Note on the Riemann Hypothesis: International Conference on Recent Developments in Mathematics (ICRDM 2022)},
  howpublished = {EasyChair Preprint 10373},
  year      = {EasyChair, 2023}}