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arXiv · 1308.3597

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

S. J. Lester
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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.

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S. J. Lester. 2013-08-16. The distribution of the logarithmic derivative of the Riemann zeta-function. https://arxiv.org/abs/1308.3597

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