Download PDFOpen PDF in browserCurrent versionCounterexample of the Riemann HypothesisEasyChair Preprint 7306, version 76 pages•Date: February 3, 2022AbstractUnder the assumption that the Riemann hypothesis is true, von Koch deduced the improved asymptotic formula $\theta(x) = x + O(\sqrt{x} \times \log^{2} x)$, where $\theta(x)$ is the Chebyshev function. We obtain a result which contradicts this asymptotic formula. By contraposition, we deduce that the Riemann hypothesis is false. Keyphrases: Chebyshev function, Nicolas inequality, Riemann hypothesis, prime numbers
