Partial zeta functions of algebraic varieties over finite fields, by Daqing Wan
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.
Daqing Wan <email@example.com>