[Math] Equivalent to Riemann Hypothesis

Question

Through last number theory, I did learn that Riemann hypothesis is equivalent to the following inequality : $|\pi(x)-Li(x)| \leq \sqrt{x} log(x)$ where $Li(x)$ is the Logarithmic integral function and $\pi(x)$ is the prime-counting function.
So, I have been more interested in it, i'd like to know more conditions which are equivalent to Riemann Hypothesis

Please, Let me know that.

Answer 1

Online lists of equivalents of the Riemann hypothesis include:

http://aimath.org/WWN/rh/ (section C, "Equivalences to RH")

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHreformulations.htm

http://en.wikipedia.org/wiki/Riemann_hypothesis#Criteria_equivalent_to_the_Riemann_hypothesis