The Poincaré series of ℂ \ ℤ

Jon Aaronson, Manfred Denker

Research output: Contribution to journalArticle

20 Scopus citations

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 languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalErgodic Theory and Dynamical Systems
Volume19
Issue number1
DOIs
StatePublished - Feb 1999

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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