Download PDFOpen PDF in browserCurrent versionA Very Brief Note on the Riemann HypothesisEasyChair Preprint 8557, version 167 pages•Date: September 14, 2022AbstractRobin'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 sumofdivisors function of $n$ and $\gamma \approx 0.57721$ is the EulerMascheroni 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 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, sumofdivisors function
