Difference between revisions of "Multiplicative function"
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Revision as of 16:30, 21 September 2006
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A multiplicative function 
is a function which commutes with multiplication. That is, 
and 
must be sets with multiplication such that 
for all 
.
Most frequently, one deals with multiplicative functions 
. These functions appear frequently in number theory, especially in analytic number theory. In this case, one sometimes also defines weak multiplicative functions: a function 
is weak multiplicative if and only if 
for all pairs of relatively prime integers 
.
