Download PDFOpen PDF in browserCurrent versionThe Riemann HypothesisEasyChair Preprint 3708, version 51Versions: 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152→history 8 pages•Date: July 9, 2021AbstractRobin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all $n > 5040$, where $\sigma(n)$ is the sumofdivisors function and $\gamma \approx 0.57721$ is the EulerMascheroni constant. This is known as the Robin inequality. We obtain a contradiction just assuming the smallest counterexample of the Robin inequality exists for some $n > 5040$. In this way, we prove that the Robin inequality is true for all $n > 5040$. Consequently, the Riemann Hypothesis is also true. Keyphrases: Divisor, inequality, number theory
