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Multiplicative Dirichlet Series
How do I go about proving that where $f(k)$ is multiplicative that: $$\sum_{k\geq 1}{\frac{f({k})}{k^{s}}}=\prod_{p}\sum_{k\geq 0}{\frac{f(p^{k})}{p^{ks}}}$$
I first tried to use the fundamental ...
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Euler product of Dirichlet Series
For $n$ a positive integer, let $f(n)$ be the squarefree part of $n$.
Find the Euler product for $\mathfrak D_{f}(s)$ where $\mathfrak D_{f}(s)$ is the Dirichlet Series of $f$.
