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(2)\ \ \frac{d}{du} \log \mathit{Z} (V,u) = \sum_{m=1}^{\infty} N_m u^{m-1}\ .</math>
In other word, the local zeta function ''Z(V,u)'' with coefficients in the [[finite field]] '''F''' is defined as a function whose [[logarithmic derivative]] generates the numbers ''N<sub>m</sub>'' of the solutions of equation, defining ''V'', in the ''m'' degree extension '''F'''<sub>''q^m''</sub>.
<!--In [[number theory]], a '''local zeta-function'''
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