  The quantization of non-Abelian gauge theories is known to be plagued by
Gribov copies. Typical examples are the copies related to zero modes of the
Faddeev-Popov operator, which give rise to singularities in the ghost
propagator. In this work we present an exact and compact expression for the
ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills
theory in the Landau gauge. It is shown, to all orders, that the condition for
the ghost propagator not to have a pole, the so-called Gribov's no-pole
condition, can be implemented by demanding a nonvanishing expectation value for
a functional of the gauge fields that turns out to be Zwanziger's horizon
function. The action allowing to implement this condition is the
Gribov-Zwanziger action. This establishes in a precise way the equivalence
between Gribov's no-pole condition and Zwanziger's horizon condition.
