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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Picard group, closed geodesics and zeta functions

Author: Mark Pollicott
Journal: Trans. Amer. Math. Soc. 344 (1994), 857-872
MSC: Primary 58F20; Secondary 11F06, 58F15, 58F17
MathSciNet review: 1240946
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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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