The Picard group, closed geodesics and zeta functions

Pollicott, Mark

doi:10.1090/S0002-9947-1994-1240946-X

The Picard group, closed geodesics and zeta functions
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Trans. Amer. Math. Soc. 344 (1994), 857-872 Request permission

Abstract:

In this article we consider the Picard group ${\text {SL}}(2,\mathbb {Z}[i])$, viewed as a discrete subgroup of the isometries of hyperbolic space. We fix a canonical choice of generators and then construct a Markov partition for the action of the group on the sphere at infinity. Our main application is to the study of the zeta function associated to the associated three-dimensional hyperbolic manifold.

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