Multiplicative function

Revision as of 19:12, 28 March 2008 by Temperal (talk | contribs) (wotw)
This is an AoPSWiki Word of the Week for March 28-April 5

A multiplicative function $f : S \to T$ is a function which commutes with multiplication. That is, $S$ and $T$ must be sets with multiplication such that $f(x\cdot y) = f(x) \cdot f(y)$ for all $x, y \in S$.

Most frequently, one deals with multiplicative functions $f : \mathbb{Z}_{>0} \to \mathbb{C}$. These functions appear frequently in number theory, especially in analytic number theory. In this case, one sometimes also defines weak multiplicative functions: a function $f: \mathbb{Z}_{>0} \to \mathbb{C}$ is weak multiplicative if and only if $f(mn) = f(m)f(n)$ for all pairs of relatively prime integers $(m, n)$. This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS