Dirichlet series

Let $z \in \mathbb{C}$. A Dirichlet series is a series of the form $$\displaystyle\sum_{k=1}^{\infty} \dfrac{a_k}{k^z}.$$

References

1915: G.H. Hardy and Marcel Riesz: The General Theory Of Dirichlet's Series ... (previous) ... (next): $I (2)$ (calls a Dirichlet series an ordinary Dirichlet series)