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In these fields, the variable ''t'' is substituted by ''p<sup>−s</sup>'', where ''s'' is the complex variable traditionally used in [[Dirichlet series]]. (For details see [[Hasse–Weil zeta function]].)
The global products of ''Z'' in the two cases used as examples in the previous section therefore come out as <math>\zeta(s)</math> and <math>\zeta(s)\zeta(s-1)</math> after letting <math>q=p</math>.
==Riemann hypothesis for curves over finite fields==
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