A type of automorphic form
The aim of this paper is to construct a Γ-automorphic form of weight −2k for a given finitely generated Fuchsian group Γ of the second kind. The construction heavily relies on important properties of the outer function introduced by Widom, which were established by the author. The constructed Γ-automorphic form possesses the highest possible smoothness for the weight −2k. Bibliography: 8 titles.
KeywordsAutomorphic Form Fuchsian Group Carleson Measure Outer Function Parabolic Element
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- 1.J. Lehner, “Discontinuous groups and automorphic functions”, in: Math. surveys, VIII, Am. Math. Soc., Providence (1964).Google Scholar