## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, J.-P. Bourguignon, M. Kotani, Y. Maeda and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 117 - 135

### On geometric analogues of Iwasawa main conjecture for a hyperbolic threefold

#### Abstract

We will discuss a relation between a special value of Ruelle–Selberg L-function of a unitary local system on a hyperbolic threefold of finite volume and Alexander invariant. A philosophy of our results are based on Iwasawa Main Conjecture in number theory.

#### Article information

**Dates**

Received: 2 August 2007

Revised: 27 September 2007

First available in Project Euclid:
28 November 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1543447905

**Digital Object Identifier**

doi:10.2969/aspm/05510117

**Mathematical Reviews number (MathSciNet)**

MR2463494

**Zentralblatt MATH identifier**

1293.11102

**Subjects**

Primary: 11F32: Modular correspondences, etc. 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

#### Citation

Sugiyama, Ken-ichi. On geometric analogues of Iwasawa main conjecture for a hyperbolic threefold. Noncommutativity and Singularities: Proceedings of French–Japanese symposia held at IHÉS in 2006, 117--135, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05510117. https://projecteuclid.org/euclid.aspm/1543447905