On Solé and Planat criterion for the Riemann Hypothesis: Mediterranean International Conference of Pure & Applied Mathematics and Related Area (MICOPAM 2023)

The 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 $\frac{1}{2}$. 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 Euler-Mascheroni constant, $\zeta(x)$ is the Riemann zeta function and $\log$ is the natural logarithm. We prove that the Riemann Hypothesis is true using this criterion.