Estimates of li(theta(x))-pi(x) and the Riemann hypothesis
Résumé
Let us denote by π(x) the number of primes x, by li(x) the logarithmic integral of x, by θ(x) = P px log p the Chebichev function and let us set A(x) = li(θ(x))−π(x). Revisiting a result of Ramanujan, we prove that the assertion "A(x) > 0 for x 11" is equivalent to the Riemann Hypothesis.
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