Resonant Interactions Along the Critical Line of the Riemann Zeta Function

Abstract

We have studied some properties of the special Gram points of the Riemann zeta function which lie on contour lines ${\bf Im}(\zeta ( s )) = 0$ which do not contain zeroes of $\zeta ( s )$. We find that certain functions of these points, which all lie on the critical line ${\bf Re}( s ) = 1/2$, are correlated in remarkable and unexpected ways. We have data up to a height of $t = 10^4$, where $s = \sigma + it$.