2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156890We will show a theorem of a type of Cheeger and Muller for a noncompact complete hyperbolic threefold of finite vulume. As an application we will compute a special value of Ruelle L-function at the origin for a unitary local system which is cuspidal.28 pagesDifferential GeometryNumber Theory11M36; 35P20; 57Q10; 58C40A special value of Ruelle L-function and the theorem of Cheeger and Mullertext