Additive function: Difference between revisions

Revision as of 03:16, 17 March 2013

Revision as of 17:20, 8 April 2013

Line 1:

{{nomore footnotes|date=February 2013}}

In [[mathematics]] the term '''additive function''' has two different definitions, depending on the specific field of application.

Line 6:

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'').

Line 98:

== Further reading ==

{{refbegin}}

* Janko Bračič, ''Kolobar aritmetičnih funkcij'' (''[[Ring (algebra)|Ring]] of arithmetical functions''), (Obzornik mat, fiz. '''49''' (2002) 4, pp. &nbsp;97–108) <span style="color:darkblue;"> (MSC (2000) 11A25) </span>

{{refend}}