Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems

Abstract In this article we prove meromorphic continuation of weighted zeta functions $$Z_f$$ Z f in the framework open hyperbolic systems by using meromorphically continued restricted resolvent Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016). We obtain a residue formula proving equality between residues invariant Ruelle distributions. combine with results et al. Lebesgue 4:81–119, 2021) order to relate Patterson–Sullivan Finally provide proof-of-principle concerning numerical calculation distributions for 3-disc scattering systems.