My question is a follow up to this question. I am curious why in the answer to the linked question, we have to assume RH to be true. Aren't all the zeros of $\zeta(0.5 + it)$ on the critical line anyways? So can we then assume that $\frac{Z'(t)}{Z(t)}$ for $t$ real is monotone between consecutive...

The question says it all. I have been researching equivalent statements on the Riemann Hypothesis, and I have not been able to find explicit upper and lower bounds on the Prime counting function (such as the ones that can be found at Dusart's and/or Axler's recent papers) such that they would imp...