The Floer homology may vanish in many variants of Floer theories; it is thus interesting to study more refined invariants of the Floer complex. For example, one may define the Reidemeister torsion of the Floer complex $\tau_F$; however, it is NOT invariant under hamiltonian isotopies. We introduce a "correction term" -- the Floer-theoretic zeta function $\zeta_F$, and show that the product $I_F=\zeta_F\tau_F$ is invariant under hamiltonian isotopies. The invariant $I_F$ can be computed in several cases, and it is also related to certain genus 1 Gromov-type invariants. Applications include existence results of lagrangian intersection points and periodic orbits (both contractible and noncontractible) in Hamiltonian dynamics.