Download PDFOpen PDF in browserCurrent versionOn Nicolas Criterion for the Riemann HypothesisEasyChair Preprint no. 10961, version 15 pages•Date: September 25, 2023AbstractThe Riemann hypothesis is the assertion that all nontrivial zeros have 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. In 1983, Nicolas stated that the Riemann hypothesis is true if and only if the inequality $\prod_{q\leq x} \frac{q}{q  1} > e^{\gamma} \cdot \log \theta(x)$ holds for all $x \geq 2$, where $\theta(x)$ is the Chebyshev function, $\gamma \approx 0.57721$ is the EulerMascheroni constant and $\log$ is the natural logarithm. In this note, using Nicolas criterion, we prove that the Riemann hypothesis is true. Keyphrases: Chebyshev function, prime numbers, Riemann hypothesis, Riemann zeta function
