2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136689For a local system on a compact hyperbolic threefold, under a cohomological assumption, we will show that the order of its twisted Alexander polynomial and of the Ruelle L function at $s=0$ coincide. Moreover we will show that their leading constant are also identical. These results may be considered as a solution of a geomeric analogue of the Iwasawa conjecture in the algebraic number theory.16 pages, no figureGeometric Topology11F32, 11M36, 57M25, 57M27text