Quantum equivalence of massive antisymmetric tensor field models in curved space

We study the effective actions in massive rank 2 and rank 3 antisymmetric tensor field models in curved space-time. These models are classically equivalent to massive vector field and massive scalar field with minimal coupling to gravity, respectively. We prove that the effective action for massive rank 2 antisymmetric tensor field is exactly equal to that for massive vector field and the effective action for massive rank 3 antisymmetric tensor field is exactly equal to that for massive scalar field. The proof is based on an identity for mass-dependent zeta functions associated with Laplacians acting on $p$ forms.