Local zeta function: Difference between revisions

Revision as of 03:31, 26 March 2018

Revision as of 09:04, 26 May 2018

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:<math>Z(V, s) = \exp\left(\sum_{m = 1}^\infty \frac{N_m}{m} (q^{-s})^m\right)</math>

where <math>N_m</math> is the number of points of <math>V</math> defined over the degree <math>m</math> extension{{explain|date=September 2017}} <math>\mathbf{F}_q_{q^m}</math> of <math>\mathbf{F}_q^m</math>, and <math>V</math> is a [[non-singular]] <math>n</math>-dimensional [[projective algebraic variety]] over the field <math>\mathbf{F}_q^m</math> with <math>q</math> elements. By the variable transformation <math>u=q^{-s}</math>, then it is defined by

:<math>