Farey Series and the Riemann Hypothesis. IV

This is a direct continuation of Part II of this series of papers and we shall not only improve (numerically) all our former results in Part II, but also prove new theorems, Theorem 4 on the function f(t) = log Γ(t+λ) and Theorem 5 for k-th power moments, k = 2,...,7, by elaborating our previous arguments. This revised version was published online in June 2006 with corrections to the Cover Date.