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: {{ #if: |{{{2}}}|G.H. Hardy}}{{#if: Marcel Riesz|{{#if: |, {{ #if: |{{{2}}}|Marcel Riesz}}{{#if: |, [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]{{#if: |, [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]}}| and [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]}}| and {{ #if: |{{{2}}}|Marcel Riesz}}}}|}}: [[Book:G.H. Hardy/The General Theory Of Dirichlet's Series{{#if: |/Volume {{{volume}}}|}}{{#if: |/{{{edpage}}}}}|The General Theory Of Dirichlet's Series{{#if: |: Volume {{{volume}}}|}}{{#if: |: {{{eddisplay}}}|{{#if: | ({{{ed}}} ed.)}}}}]]{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}{{#if: |, {{{publisher}}}|}}{{#if: |, ISBN {{{isbn}}}|}}{{#if: General Dirichlet series | ... (previous)|}}{{#if: findme | ... (next)|}}{{#if: |: Entry: {{#if: |[[{{{entryref}}}|{{{entry}}}]]|{{{entry}}}}}|}}: $I.1.(2)$ (calls a Dirichlet series an ordinary Dirichlet series)