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Abstract
Under 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.
