Abstract
We show that the Poincaré series of the Fuchsian group of deck transformations of ℂ \ ℤ diverges logarithmically. This is because ℂ \ ℤ is a ℤ-cover of the three horned sphere, whence its geodesic flow has a good section which behaves like a random walk on ℝ with Cauchy distributed jump distribution and has logarithmic asymptotic type.
Original language | English (US) |
---|---|
Pages (from-to) | 1-20 |
Number of pages | 20 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 19 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1999 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics