The series is convergent when s is a complex number with <(s) > 1. Some special values of ζ(s) are well known, for example the values ζ(2) = π/6, ζ(4) = π/90, were obtained by Euler. In 1859, Riemann had the idea to define ζ(s) for all complex number s by analytic continuation. This continuation is very important in number theory and plays a central role in the study of the distribution of prim...
