The Poincaré series of $\mathbb C\setminus\mathbb Z$
1999 ◽
Vol 19
(1)
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pp. 1-20
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Keyword(s):
We show that the Poincaré series of the Fuchsian group of deck transformations of ${\mathbb C}\setminus{\mathbb Z}$ diverges logarithmically. This is because ${\mathbb C}\setminus{\mathbb Z}$ is a ${\mathbb Z}$-cover of the three horned sphere, whence its geodesic flow has a good section which behaves like a random walk on ${\mathbb R}$ with Cauchy distributed jump distribution and has logarithmic asymptotic type.
1989 ◽
Vol 32
(1)
◽
pp. 131-137
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Keyword(s):
Keyword(s):
2011 ◽
Vol 59
(11)
◽
pp. 1189-1199
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2014 ◽
Vol 28
(1)
◽
pp. 191-225
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1994 ◽
Vol 95
(3)
◽
pp. 271-295
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