The product theorem for parametrized homotopy Reidemeister torsion

The goal of this article is to prove the product formula for parametrized homotopy Reidemeister torsion. The theorem states that the product of the parametrized Euler characteristic of one fibration with the parametrized Reidemeister torsion class of another fibration yields the parametrized Reidemeister torsion class of the product fibration. In the process of establishing the theorem, several new products must be defined involving (derivative theories of) parametrized A-theory and a detailed description of the coassembly map for parametrized A-theory is included.