Counterexample of the Riemann Hypothesis

EasyChair Preprint 7306, version 7

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, Riemann hypothesis, prime numbers

@booklet{EasyChair:7306,
  author    = {Frank Vega},
  title     = {Counterexample of the Riemann Hypothesis},
  howpublished = {EasyChair Preprint 7306},
  year      = {EasyChair, 2022}}