Notes on the Phase Statistics of the Riemann Zeros

Abstract

We numerically investigate, for zeros $\rho =1/2+i\gamma$, the statistics of the imaginary part of $\log ({\zeta }^{\prime }(1/2+i\gamma ))$, computed by continuous variation along a vertical line from $\sigma =4$ to $4+i\gamma$ and then along a horizontal line to $1/2+i\gamma$.