Meromorphic solutions of a system of functional equations involving the modular group
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- by Michael M. Brady PDF
- Proc. Amer. Math. Soc. 30 (1971), 271-277 Request permission
Abstract:
The purpose of this paper is to study the meromorphic solutions F of the system of functional equations (1) $F[T(z)] = T[F(z)]$ , for all T in the modular group M and z in the upper-half plane. A formula is given which expresses all such solutions explicitly in terms of the functions automorphic relative to M. Then, an application of the functions that satisfy (1) is given, and some observations are made concerning solutions of the more general system of functional equations that results when M is replaced by an arbitrary Fuchsian group.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 271-277
- MSC: Primary 30.49; Secondary 39.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280712-5
- MathSciNet review: 0280712