Additive function (math.)
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Additive function Definition from Encyclopedia Dictionaries & Glossaries
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Additive function
Different definitions exist depending on the specific field of application. Traditionally, an additive function is a function that preserves the addition operation:
- f(x+y) = f(x)+f(y)
In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime, the function of the product is the sum of the functions:
- f(ab) = f(a) + f(b).
The remainder of this article discusses number theoretic additive functions, using the second definition. For a specific case of the first definition see additive polynomial. Note also that any homomorphism f between Abelian groups is "additive" by the first definition.
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