Local zeta function: Difference between revisions

Revision as of 08:40, 7 September 2017

Revision as of 08:56, 7 September 2017

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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''_''m'' is the number of points of ''V'' defined over the degree ''m'' extension{{what's this?explain}} '''F'''_''q''^''m'' of '''F'''_''q'', and ''V'' is a [[non-singular]] ''n''-dimensional [[projective algebraic variety]] over the field '''F'''_''q'' with ''q'' elements. By the variable transformation <math>u=q^{-s}</math>, then it is defined by

:<math>