Applications
The zeta function occurs in applied statistics (see Zipf's law and Zipf–Mandelbrot law).
Zeta function regularization is used as one possible means of regularization of divergent series in quantum field theory. In one notable example, the Riemann zeta-function shows up explicitly in the calculation of the Casimir effect. The zeta function is also useful for the analysis of dynamical systems.
Read more about this topic: Riemann Zeta Function