  The special uniformity of zeta functions claims that pure non-abelian zeta
functions coincide with group zeta functions associated to the special linear
groups. Naturally associated are three aspects, namely, the analytic,
arithmetic, and geometric aspects. In the first paper of this series, we expose
intrinsic geometric structures of our zetas by counting semi-stable bundles on
curves defined over finite fields in terms of their automorphism groups and
global sections. We show that such a counting maybe read from Artin zetas which
are abelian in nature. This paper also contains an appendix written by H.
Yoshida, one of the driving forces for us to seek group zetas. In this
appendix, Yoshida introduces a new zeta as a function field analogue of the
group zeta for SL2 for number fields and establishes the Riemann Hypothesis for
it.
