For a definition of effective ergodic transformation
see Gacs et al.
The first approach to investigate the value distribution of the Riemann zeta function by using an ergodic transformation was done by Steuding.
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. In [LW09], M.
A Poisson qso with two different parameters is a regular and, respectively, ergodic transformation with respect to strong convergence.
A Poisson qso with three different parameters is a regular and, respectively, ergodic transformation with respect to strong convergence.
Applying the "ergodic transformation", after some algebra we find that in such a space the metric d[s.sup.2] takes the form [(dagger)]
As such, dt should be expressed through the ergodic transformation d[x.sup.i] = [v.sup.i]dt = ([[bar.v].sup.i] + [??]].sup.i])dt.
While a particle is moved along d[x.sup.i] by an external force (or several forces), the acceleration gained by the particle is determined by the fact that its spatial impulse vector [p.sup.i], being transferred along d[x.sup.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.