Convergent Riemann zeta function. Try to play it.
The button in the lower left corner starts the animation of the value of the imaginary part of (s).
Try to start it, you can take advantage of it to count how many times the convergence point of the zeta (s) function passes through the origin of the plane (if a=0.5).
To find out more, you can read an article of mine published on zenodo.org http://doi.org/10.5281/zenodo.6654333
Thanks to GeoGebra's zeta(x) function I added the convergence point (green) of the Riemann zeta function; calculated according to the values (a) and (b) controlled by the two sliders.
I also propose this article.
The zeta(s) function. Endless spirals in search of their origin.
http://doi.org/10.5281/zenodo.6686105