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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of a theorem of Poincaré
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by Irwin Kra PDF
Proc. Amer. Math. Soc. 27 (1971), 299-302 Request permission

Abstract:

Let $G$ be a finitely generated Fuchsian group of the first kind. Let $\varphi$ be a cusp form, and $f$ a solution to ${\theta _2}f = \varphi$, where ${\theta _2}$ is the Schwarzian derivative. Then for every $A \in G$ there is a Möbius transformation $\chi (A)$ such that $f \circ A = \chi (A) \circ f$. We show that the homomorphism $\chi$ from $G$ to Möbius transformations determines $\varphi$. The theorem for the special case where $G$ is the covering group of a compact surface was first proved by Poincaré.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 299-302
  • MSC: Primary 30A58; Secondary 20H10
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0301189-7
  • MathSciNet review: 0301189