  Let f be a regular function on a nonsingular complex algebraic variety of
dimension d. We prove a formula for the motivic zeta function of f in terms of
an embedded resolution. This formula is over the Grothendieck ring itself, and
specializes to the formula of Denef and Loeser over a certain localization. We
also show that the space of n-jets satisfying f=0 can be partitioned into
locally closed subsets which are isomorphic to a cartesian product of some
variety with an affine space of dimension the round up of dn/2. Finally, we
look at the consequences for the poles of the motivic zeta function.
