Partial zeta functions of algebraic varieties over finite fields

Details Partial zeta functions of algebraic varieties over finite fields Partial zeta functions of algebraic varieties over finite fields

2000-06-14

arxiv.org/abs/math/0006236v1

Mathematics

Number Theory

Scientific paper

By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well known rationality theorem. In general, the partial zeta function is probably not rational. But a theorem of Faltings says that the partial zeta function is always nearly rational.

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