Additive function: Difference between revisions

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for any two elements ''x'' and ''y'' in the ___domain. For example, any [[linear map]] is additive. When the ___domain is the [[real numbers]], this is [[Cauchy's functional equation]].

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<ref name="Erdos1939">Erdös, P., and M. Kac. On the Gaussian Law of Errors in the Theory of Additive Functions. Proc Natl Acad Sci USA. 1939 April; 25(4): 206–207. [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1077746/ online]</ref>:

:''f''(''ab'') = ''f''(''a'') + ''f''(''b'').

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== See also ==

* [[Sigma additivity]]

==References==

{{Reflist}}

== Further reading ==