**Definition**: Arithmetic Function

A function $f:\mathbb Z \mapsto \mathbb C$ is called **arithmetic** (another name: **number-theoretic**).

### Notes

- The domain of arithmetic functions is the set of integers $\mathbb Z.$
- The codomain of arithmetic functions can be integers $\mathbb Z,$ real numbers $\mathbb R,$ or even complex numbers $\mathbb C.$

| | | | | created: 2019-03-17 18:08:16 | modified: 2019-06-15 08:50:47 | by: *bookofproofs* | references: [701], [1272]

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[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

[701] **Scheid Harald**: “Zahlentheorie”, Spektrum Akademischer Verlag, 2003, 3. Auflage

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