A Very Brief Note on the Riemann Hypothesis

Frank Vega
2022 Zenodo  
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
more » ... e 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.
doi:10.5281/zenodo.7078919 fatcat:ktrp3ht5ujdl5icqki5f56ypai