Evidence of Long Range Order in the Riemann Zeta Function

Abstract

We have done a statistical analysis of some properties of the contour lines Im$(\zeta (s))$ = 0 of the Riemann zeta function. We find that this function is broken up into strips whose average width on the critical line does not appear to vary with height. We also compute the position of the primary zero for the lowest 200 strips, and find that this probability distribution also appears to be scale invariant.