The Poincare series of C backslash Z

Authors
Aaronson, J Denker, M
Citation
J. Aaronson et M. Denker, The Poincare series of C backslash Z, ERGOD TH DY, 19, 1999, pp. 1-20
Citations number
26
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
19
Year of publication
1999
Part
1
Pages
1 - 20
Database
ISI
SICI code
0143-3857(199902)19:<1:TPSOCB>2.0.ZU;2-1
Abstract
We show that the Poincare series of the Fuchsian group of deck transformati ons of C \ Z diverges logarithmically. This is because ct: \ Z is a Z-cover of the three horned sphere, whence its geodesic flow has a good section wh ich behaves like a random walk on R with Cauchy distributed jump distributi on and has logarithmic asymptotic type.