Meromorphic functions that share four values
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- by Gary G. Gundersen
- Trans. Amer. Math. Soc. 277 (1983), 545-567
- DOI: https://doi.org/10.1090/S0002-9947-1983-0694375-0
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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
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Bibliographic 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