Problems in Analytic Number Theory pp 3-15 | Cite as

# Arithmetic Functions

Chapter

## Abstract

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**arithmetic function***f*is a complex-valued function defined on the natural numbers. Such an*f*is called an**additive function**if$$ f(mn) = f(m) + f(n) $$

(1.1)

*m*and*n*are coprime. If (1.1) holds for all*m, n*, then*f*is called**completely additive**.**A multiplicative**function is an arithmetic function*f*satisfying*f*(l) = 1 and$$ f(mn) = f(m)f(n) $$

(1.2)

*m*and*n*are coprime. If (1.2) holds for all*m, n*, then*f*is called**completely multiplicative**.## Keywords

Prime Number Prime Divisor Inversion Formula Multiplicative Function Average Order
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 2001