Fried conjecture for twisted Ruelle zeta functions of Anosov flows

Let $M$ be a closed $3$-manifold, let $\varphi$ be a smooth transitive Anosov flow on $M$, and let $\rho$ be an acyclic unitary representation of $\pi_1(M)$. Define the twisted Ruelle zeta function, initially for $\operatorname{Re} s\gg 1$, by

$$\zeta_{\varphi,\rho}(s)=\prod_{\gamma\text{ primitive closed orbit of }\varphi}\det\bigl(I-e^{-sT_\gamma}\Delta_\gamma\rho(\gamma)\bigr),$$

where $T_\gamma$ is the length of $\gamma$ and $\Delta_\gamma=\pm1$ depends on the orientation of the unstable bundle over $\gamma$. The product admits a meromorphic continuation to $\mathbb{C}$. Fried conjecture. The number $|\zeta_{\varphi,\rho}(0)|^{-1}$ is a topological invariant of $M$, namely the $\rho$-twisted Reidemeister torsion of $M$.