  We give an example of a real algebraic manifold embedded in a complex space
that does not satisfy the Nash-Artin approximation Property. This Nash-Artin
approximation Property is closely related to the problem of determining when
the biholomorphic equivalence for germs of real algebraic manifolds coincides
with the algebraic equivalence. This example is an elliptic Bishop surface, and
its construction is based on the functional equation satisfied by the
generating series of some walks restricted to the quarter plane.
