Meromorphic solutions of a system of functional equations involving the modular group-Reference-Cited by-同舟云学术

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

Published:1971 Issue:2 Volume:30 Page:271-277
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Brady Michael M.

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 ) ] 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-030-02/S0002-9939-1971-0280712-5/S0002-9939-1971-0280712-5.pdf

Reference6 articles.

1. Meromorphic solutions of a system of functional equations involving the modular group;Brady, Michael M.;Proc. Amer. Math. Soc.,1971

2. L. Ford, Automorphic functions, McGraw-Hill, New York, 1929.

3. On the pseudoperiods of the Weierstrass zeta functions;Heins, Maurice;SIAM J. Numer. Anal.,1966

4. \bysame, On the pseudoperiods of the Weierstrass zeta-functions. II, Nagoya Math. J. 30 (1967).

5. Monografie Matematyczne, Tom 28;Saks, Stanisław,1965

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