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:<math>Z(V, s) = \exp\left(\sum_{m = 1}^\infty \frac{N_m}{m} (q^{-s})^m\right)</math>
where ''N''<sub>''m''</sub> is the number of points of ''V'' defined over the degree ''m'' extension{{explain|date=September 2017}} '''F'''<sub>''q''<sup>''m''</sup></sub> of '''F'''<sub>''q''</sub>, and ''V'' is a [[non-singular]] ''n''-dimensional [[projective algebraic variety]] over the field '''F'''<sub>''q''</sub> with ''q'' elements. By the variable transformation <math>u=q^{-s}</math>, then it is defined by
:<math>
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