The distribution of the logarithmic derivative of the Riemann zeta-function

Abstract

We investigate the distribution of the logarithmic derivative of the Riemann zeta-function on the line Re(s)=σ, where σ, lies in a certain range near the critical line σ=1/2. 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.

arXiv comment21 pages

Cited by in corpus (1)

• Almost all of the zeros of the Riemann zeta-function are on the critical line