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where the sum extends over all monic [[divisor]]s ''d'' of ''m'', or equivalently over all pairs (''a'', ''b'') of monic polynomials whose product is ''m''.
The identity <math>D_{h}D_{g}=D_{h*g}</math> still holds. Thus, like in the elementary theory, the polynomial Dirichlet series and the zeta function has a connection with the notion of mean values in the context of polynomials. The following examples illustrate it.
===Examples===▼
====The density of the k-th power free polynomials in {{math|F<sub>q</sub>[X]}}====
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And since it doesn't depend on ''n'' this is also the mean value of <math>\delta(f)</math>.
▲===Examples===
====Polynomial Divisor functions====
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