Meromorphic functions that share four values
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- by Gary G. Gundersen PDF
- Trans. Amer. Math. Soc. 277 (1983), 545-567 Request permission
Correction: Trans. Amer. Math. Soc. 304 (1987), 847-850.
Abstract:
An old theorem of ${\text {R}}$. Nevanlinna states that if two distinct nonconstant meromorphic functions share four values counting multiplicities, then the functions are Möbius transformations of each other, two of the shared values are Picard values for both functions, and the cross ratio of a particular permutation of the shared values equals -1. In this paper we show that if two nonconstant meromorphic functions share two values counting multiplicities and share two other values ignoring multiplicities, then the functions share all four values counting multiplicities.References
- W. W. Adams and E. G. Straus, Non-archimedian analytic functions taking the same values at the same points, Illinois J. Math. 15 (1971), 418–424. MR 277771
- Gary G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc. (2) 20 (1979), no. 3, 457–466. MR 561137, DOI 10.1112/jlms/s2-20.3.457
- Gary G. Gundersen, Meromorphic functions that share two finite values with their derivative, Pacific J. Math. 105 (1983), no. 2, 299–309. MR 691606
- W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038 R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.
- Hans Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 8, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). MR 0077620
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 277 (1983), 545-567
- MSC: Primary 30D35
- DOI: https://doi.org/10.1090/S0002-9947-1983-0694375-0
- MathSciNet review: 694375