Local zeta function: Difference between revisions

Revision as of 19:13, 5 June 2015

Revision as of 19:14, 5 June 2015

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Suppose that ''V'' is a [[non-singular]] ''n''-dimensional [[projective algebraic variety]] over the field '''F'''_''q'' with ''q'' elements. In [[number theory]], the '''local zeta function''' ''Z''(''V'', ''s'') of ''V'' (or, sometimes called the '''congruent zeta function''') is defined as

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