Completely multiplicative function: Difference between revisions

Revision as of 14:41, 15 March 2013

Revision as of 10:21, 3 January 2014

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\end{align}

</math>

===Dirichlet series===

Moreover, The L-function of completely (or totally) [[multiplicative function|multiplicative]] [[Dirichlet series]] a(n) satisfies

:<math>L(s,a)=\sum^\infty_{n=1}\frac{a(n)}{n^s}=\prod_p\biggl(1-\frac{a(p)}{p^s}\biggr)^{-1},</math>

which means that the sum all over the natural numbers is equal to the product all over the prime numbers.

==See also==