Poincaré series and teichmüller space
作者:
Makoto Masumoto,
期刊:
Complex Variables, Theory and Application: An International Journal
(Taylor Available online 1993)
卷期:
Volume 21,
issue 1-2
页码: 1-7
ISSN:0278-1077
年代: 1993
DOI:10.1080/17476939308814609
出版商: Gordon and Breach Science Publishers
关键词: 32G15
数据来源: Taylor
摘要:
We consider the Poincaré series operator Θ as a holomorphic mapping of the Teichmüller space T(Γ) of a Fuchsian group Γ into the Bers spaceA(Γ) of integrable holomorphic quadratic forms, and show that if Γ is finitely generated and of the first kind, then ⊖ gives a local coordinate ofT(Γ) at the origin. Conversely, if Θ(T(Γ)) contains an interior point in A(Γ), then Γ is finitely generated and of the first kind.
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