We prove, as an analogy of a conjecture of Artin, that if $ Y \rightarrow X $ is a finite flat morphism between two singular reduced absolutely irreducible projective algebraic curves defined over a finite field, then the numerator of the zeta function of X divides that of Y in $ \mathbb{Z}[T] $ . Then, we give some interpretations of this result in terms of semi-abelian varieties.