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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Meromorphic solutions of a system of functional equations involving the modular group


Author: Michael M. Brady
Journal: Proc. Amer. Math. Soc. 30 (1971), 271-277
MSC: Primary 30.49; Secondary 39.00
MathSciNet review: 0280712
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280712-5
PII: S 0002-9939(1971)0280712-5
Keywords: Functional equations, modular group, automorphic functions, pseudoperiodic functions, Fuchsian group, Weierstrass zeta-function
Article copyright: © Copyright 1971 American Mathematical Society