Download PDFOpen PDF in browserCurrent versionOn Nicolas Criterion for the Riemann HypothesisEasyChair Preprint 10961, version 28 pages•Date: October 23, 2023AbstractThe Riemann hypothesis is the assertion that all nontrivial zeros are 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. 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 the Nicolas criterion, we prove that the Riemann hypothesis is true. Keyphrases: Chebyshev function, Riemann hypothesis, Riemann zeta function, prime numbers
