A-points of the zeta function: A generalization of the zeros of the zeta function

The solutions of equation \zeta (z)-a=0,\text a\in \mathbb{C} are generally referred to as A-points of the zeta function. A-points therefore represent a generalization of the zeros of the zeta function. The special case of a=0 applies to the ‘normal’ zeros of the zeta function.

The following video shows that the distinction between ‘trivial’ (along the negative X-axis) and ‘non-trivial’ zeros (along the ‘critical’ line with real part 1/2) makes only sense  for the case a=0.

An animation created by varying the parameter a rather shows a smooth transition between the ‘trivial’ A-points and the ‘non-trivial’ A-points:

Sound: Sebastian Kuhl