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The Polynomial [[von Mangoldt function]] is defined by:
<math>\Lambda_{A}(f) = \begin{cases} \log |P| & \mbox{if }f=|P|^k \text{ for some prime monic} P \text{ and integer } k \ge 1, \\ 0 & \mbox{otherwise.} \end{cases}</math>
Where the logarithm is taken on the basis of ''q''.
'''Proposition.''' The mean value of <math>\Lambda_{A}</math> is exactly <math>\log(q)</math>.
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<math>\sum_{deg(m)=n}\Lambda_{A}(m)=q^{n}log(q)</math>,<br /> and by dividing by <math>q^n</math> we get that,
<math>Ave_{n}\Lambda_{A}(m)=log(q)=1</math>.
====Polynomial Euler totient function====
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