Local zeta function: Difference between revisions

Revision as of 20:03, 2 October 2019

Revision as of 01:29, 16 September 2020

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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''}} is the number of points of {{mvar|''V''}} defined over the {{math|''m''^th}} [[cyclotomicfinite field|cyclotomic]] [[field extension]]{{explain|date=September 2017}} {{math|'''F'''_''q''^''m''}} of {{math|'''F'''_''q'',}} and {{mvar|V}} is a [[non-singular]] {{mvar|n}}-dimensional [[projective algebraic variety]] over the field {{math|'''F'''_''q''}} with {{mvar|q}} elements. By the variable transformation {{math|''u''&nbsp;{{=}}&nbsp;''q''^−''s'',}} then it is defined by

:<math>

\mathit{Z} (V,u) = \exp