Download PDFOpen PDF in browserCurrent versionOn Solé and Planat Criterion for the Riemann HypothesisEasyChair Preprint no. 10519, version 136 pages•Date: August 25, 2023AbstractThere are several statements equivalent to the famous Riemann hypothesis. In 2011, Solé and Planat stated that the Riemann hypothesis is true if and only if the inequality $\zeta(2) \cdot \prod_{q\leq q_{n}} (1+\frac{1}{q}) > e^{\gamma} \cdot \log \theta(q_{n})$ holds for all prime numbers $q_{n}> 3$, where $\theta(x)$ is the Chebyshev function, $\gamma \approx 0.57721$ is the EulerMascheroni constant, $\zeta(x)$ is the Riemann zeta function and $\log$ is the natural logarithm. In this note, using Solé and Planat criterion, we prove that the Riemann hypothesis is true. Keyphrases: Chebyshev function, prime numbers, Riemann hypothesis, Riemann zeta function
