The Riemann Zeta Function along the Critical Line скачать в хорошем качестве

The Riemann Zeta Function along the Critical Line

The video shows characteristics of the Riemann zeta function zeta(z) in a strip containing the critical line. The imaginary part of z increases to the right and the real part increases upward. The blue curves are the nodal lines of Re(zeta(z)) = 0 and the red curves are the nodal lines of Im(zeta(z)) = 0. The two sets of curves intersect at the nontrivial zeros on the critical line. The ocher-colored regions are the pre-images of the unit disk, |(zeta(z))]＜1. By Voronin's universality theorem, a wide variety of shapes of the ocher regions can be observed.