Local zeta function: Difference between revisions

Revision as of 09:17, 26 May 2018

Revision as of 09:21, 26 May 2018

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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 ''<math>Z(V,u)''</math> with coefficients in the [[finite field]] '''<math>\mathbf{F'''}_q</math> is defined as a function whose [[logarithmic derivative]] generates the numbers ''N_m'' of the solutions of equation, defining ''V'', in the ''m'' degree extension '''F'''<submath>''\mathbf{F}_{q^m''}</submath>.

<!--In [[number theory]], a '''local zeta-function'''