Counterexample of the Riemann Hypothesis

EasyChair Preprint no. 7306, version 7

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6 pagesDate: February 3, 2022

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.

Keyphrases: Chebyshev function, Nicolas inequality, prime numbers, Riemann hypothesis