[math-fun] Zeroes of Riemann Zeta and Estimates of Prime-counting Functions

Can anyone recommend a relatively easy discussion of how the location of zeroes of the Riemann zeta function affect estimates of prime-counting functions? Specifically I have two questions. 1. What would happen if there were zeroes on (for example) the line Re(s) = .75? 2. We know that the first umpteen billion zeroes are on Re(s) = 1/2, with Im(s) < T. As we compute more zeroes, this bound T gets larger. How exactly does this improve estimates for Pi(x), Theta(x), and Psi(x) ? Bob Baillie