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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 $\mathbb C.$

Mentioned in:

Definitions: 1 2 3 4 5 6 7 8 9
Examples: 10
Proofs: 11 12
Propositions: 13 14

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References

Bibliography

1. Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
2. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927