Resonant Interactions Along the Critical Line of the Riemann Zeta Function

Ronald Fisch

Published 2013-09-18, updated 2013-11-11Version 2

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 $s = \sigma + it$.