The full name is Riemann Zeta Function. It's defined as:
One of its uses is as a comparison series for testing convergence however it is also related to the distribution of prime numbers and quantum systems energy levels. You can find
full discussion of Riemann Zeta Function in this website by Xavier Gourdon and Pascal Sebah, or in the books listed to the left.
Taylan Akdogan, Physics Grad Student, MIT, Cambridge