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Dirichlet series for complex powers of the Riemann zeta function

By Winston Alarcon-Athens
In order to obtain the Dirichlet series for the exponential ζ(s)z\zeta(s)^z, we define and study the basic properties a sequence (αn(z))nZ+(\alpha_n(z))_{n \in {\Bbb Z}^+} of polynomials in the indeterminate zz which, being used as coefficients of the respective terms of the Dirichlet series of ζ(s)\zeta(s) in the semi-plane (s)>1\Re(s)>1, they... Show more
January 26, 2021
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Dirichlet series for complex powers of the Riemann zeta function
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