Download PDFOpen PDF in browserCurrent versionAn Equivalent to the Riemann HypothesisEasyChair Preprint 11528, version 48 pages•Date: December 18, 2023AbstractThe Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis. 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 sumofdivisors function of $n$, $\gamma \approx 0.57721$ is the EulerMascheroni constant and $\log$ is the natural logarithm. We prove that the Riemann hypothesis is true whenever there exists a large enough positive number $x_{0}$ such that for all $x > x_{0}$ we obtain the approximate value of Keyphrases: Riemann hypothesis, Robin's criterion, Superabundant numbers, prime numbers
