The first approach to investigate the value distribution of the Riemann zeta function by using an ergodic transformation was done by Steuding.
We are interested in studying the value distribution of not only the Riemann zeta function itself, but also its derivatives, on the vertical lines [sigma] + iR with respect to a more general ergodic transformation, which we shall call affine Boolean transformation [T.
Steuding, Sampling the Lindelof hypothesis with an ergodic transformation, in Functions in number theory and their probabilistic aspects, RIMS Kokyuroku Bessatsu, B34, Res.
Our second result is related to the value distribution of the Riemann zeta function and its derivatives which is obtained by using ergodic transformations.
As such, dt should be expressed through the ergodic transformation d[x.
i], undergoes a space-time turn dt expressed by the ergodic transformation (17).
Therefore, for the entire motion of a particle, we have no need of expanding [partial derivative]/[partial derivative]t by the ergodic transformation, for each force acting thereon.