Dirichlet Series of Convolution of Arithmetic Functions
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Theorem
Let $f, g: \N \to \C$ be arithmetic functions.
Let $h = f * g$ be their Dirichlet convolution.
Let $F, G, H$ be their Dirichlet series.
Let $s$ be a complex number such that $\map F s$ and $\map G s$ converge absolutely.
Then $\map H s$ converges absolutely to $\map F s \times \map G s$.
Proof
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