THE DISTRIBUTION OF THE LOGARITHMIC DERIVATIVE OF THE RIEMANN ZETA-FUNCTION

We investigate the distribution of the logarithmic derivative of the Riemann zeta-function on the line ℜ(s)=σ, where σ lies in a certain range near the critical line σ=½. For such σ, we show that the distribution of ζ′/ζ(s) converges to a two-dimensional Gaussian distribution in the complex plane. Upper bounds on the rate of convergence to the Gaussian distribution are also obtained.