It is known that the zeta function is rational in the case of Markov bilateral subshifts of finite type, and therefore for any C1 diffeomorphism on a hyperbolic set with local product structure. Besides, in both cases, the radius of convergence is related to the topological entropy. We will prove that these two properties are also true for the unilateral subshifts of finite type and, in general, for any Ruelle-expanding map.