An analog of the Iwasawa conjecture for a complete hyperbolic threefold of finite volume

Abstract

For a unitary local system of rank one on a complete hyperbolic threefold of finite volume which has only one cusp, we will compare the order of the Alexander invariant at t=1 and one of Ruelle-Selberg L-function at s=0. Our result may be considered as a geometric analog of the Iwasawa main conjecture in the algebraic number theory.

27 pages

Cited by in corpus (2)

• Analogies between Knots and Primes, 3-Manifolds and Number Rings
• A special value of Ruelle L-function and the theorem of Cheeger and Muller