  In this paper, we introduce and study two new types of non-abelian zeta
functions for curves over finite fields, which are defined by using (moduli
spaces of) semi-stable vector bundles and non-stable bundles. A Riemann-Weil
type hypothesis is formulated for zeta functions associated to semi-stable
bundles, which we think is more canonical than the other one. All this is
motivated by (and hence explains in a certain sense) our work on non-abelian
zeta functions for number fields.
