An analog of the Iwasawa conjecture for a compact hyperbolic threefold

Abstract

For 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.