Part of the Graduate Texts in Mathematics book series (GTM, volume 206)
An arithmetic function f is a complex-valued function defined on the natural numbers. Such an f is called an additive function if
whenever 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
$$ f(mn) = f(m) + f(n) $$
whenever m and n are coprime. If (1.2) holds for all m, n, then f is called completely multiplicative.
$$ f(mn) = f(m)f(n) $$
KeywordsPrime 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.
Unable to display preview. Download preview PDF.
© Springer Science+Business Media New York 2001