Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

On meromorphic functions commuting with elements of a function group


Author: John Roderick Smart
Journal: Proc. Amer. Math. Soc. 33 (1972), 343-348
MSC: Primary 30A58
DOI: https://doi.org/10.1090/S0002-9939-1972-0293086-1
MathSciNet review: 0293086
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The problem of whether there always exist meromorphic functions commuting with all substitutions of a function group is solved in the affirmative.


References [Enhancements On Off] (What's this?)

  • [1] M. Brady, Meromorphic solutions of a system of functional equations involving the modular group, Proc. Amer. Math. Soc. 30 (1971), 271-277. MR 0280712 (43:6431)
  • [2] Lester R. Ford, Automorphic functions, McGraw-Hill, New York, 1929.
  • [3] R. Fricke, Die elliptishe Funktionen und ihre Anwendungen. I, Teubner, Leipzig, 1916.
  • [4] M. Heins, On the pseudoperiods of the Weierstrass zeta functions, SIAM J. Numer. Anal. 3 (1966), 266-268. MR 34 #4548. MR 0204710 (34:4548)
  • [5] -, On the pseudo-periods of the Weierstrass zeta functions. II, Nagoya Math. J. 30 (1967), 113-119. MR 41 #7098. MR 0262492 (41:7098)
  • [6] A. Hurwitz, Grundlagen einer independenten Theorie der elliptischen Modulfunktionen und die Theorie der Multiplikator-Gleichungen erster Stufe, Math. Ann. 18 (1881), 528-592; Werke. I, Basel, 1932, pp. 1-66.
  • [7] -, Über die Theorie der elliptischen Modulfunktionen, Math. Ann. 58 (1904), 343-360; Werke. I, Basel, 1932, pp. 577-595. MR 1511237
  • [8] J. Lehner, Discontinuous groups and automorphic functions, Math. Surveys, no. 8, Amer. Math. Soc., Providence, R. I., 1964. MR 29 #1332. MR 0164033 (29:1332)
  • [9] S. Saks and A. Zygmund, Analytic functions, 2nd ed., PWN, Warsaw, 1965. MR 31 #4889. MR 0180658 (31:4889)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A58

Retrieve articles in all journals with MSC: 30A58


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0293086-1
Keywords: Automorphic form, Fuchsian group, Kleinen group, Weierstrass zeta function, modular group, Dedekind eta function
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society