The Riemann Zeta Function

For Re s = σ > 1, theRiemann zeta function ζ(s)is defined by $$ \zeta \left( s \right) = \sum\limits_{n = 1}^\infty {\frac{1}{{{n^s}}}} . $$ It follows from the definition that ζ(s) is an analytic function in the half-plane Re s > 1.