In the first two sections of the present chapter we introduce a conjecture (Conjecture 7.1) which specifies the idea that the characterization of the divisor of the Selberg zeta function of the a-twisted geodesic flow proved in Chapter 3 Section 3.3 is related to its characterizations in terms of a-twisted harmonic currents on SX. In the third section we prove some results on a-twisted globally harmonic currents which are constant along the leaves of 03—. In addition to the results in Chapter 5 these results support Conjecture 7.1. Moreover, in Section 7.4 we give a complete description of the divisor of the Ruelle zeta function Z of the geodesic flow of a compact hyperbolic 4-manifold X in terms of harmonic currents on SX. The appropriate notion of harmonicity involves additional conditions along the leaves of P.