Dirichlet series for complex powers of the Riemann zeta function

In order to obtain the Dirichlet series for the exponential \zeta(s)^z, we define and study the basic properties a sequence (\alpha_n(z))_{n \in {\Bbb Z}^+} of polynomials in the indeterminate z which, being used as coefficients of the respective terms of the Dirichlet series of \zeta(s) in the semi-plane \Re(s)>1, they... Show more