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An analog of the Iwasawa conjecture for a compact hyperbolic threefold

Ken-ichi Sugiyama
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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.

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Ken-ichi Sugiyama. 2007-08-27. An analog of the Iwasawa conjecture for a compact hyperbolic threefold. https://arxiv.org/abs/math/0606010

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