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
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