Difference between revisions of "Dirichlet series"
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$$\displaystyle\sum_{k=1}^{\infty} \dfrac{a_k}{k^z}.$$ | $$\displaystyle\sum_{k=1}^{\infty} \dfrac{a_k}{k^z}.$$ | ||
| − | + | =Properties= | |
| − | ==References | + | =General Dirichlet series= |
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| + | =References= | ||
{{BookReference|The General Theory Of Dirichlet's Series|1915|G.H. Hardy|author2=Marcel Riesz|prev=General Dirichlet series|next=findme}}: $I.1.(2)$ (calls a Dirichlet series an <i>ordinary</i> Dirichlet series) | {{BookReference|The General Theory Of Dirichlet's Series|1915|G.H. Hardy|author2=Marcel Riesz|prev=General Dirichlet series|next=findme}}: $I.1.(2)$ (calls a Dirichlet series an <i>ordinary</i> Dirichlet series) | ||
[[Category:Definition]] | [[Category:Definition]] | ||
Latest revision as of 23:27, 17 March 2017
Let $z \in \mathbb{C}$. A Dirichlet series is a series of the form $$\displaystyle\sum_{k=1}^{\infty} \dfrac{a_k}{k^z}.$$
Properties
General Dirichlet series
References
1915: G.H. Hardy and Marcel Riesz: The General Theory Of Dirichlet's Series ... (previous) ... (next): $I.1.(2)$ (calls a Dirichlet series an ordinary Dirichlet series)
