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Transactions of the American Mathematical Society

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Meromorphic functions that share four values


Author: Gary G. Gundersen
Journal: Trans. Amer. Math. Soc. 277 (1983), 545-567
MSC: Primary 30D35
MathSciNet review: 694375
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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 [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0694375-0
Keywords: Meromorphic functions, distribution of values, Nevanlinna theory, shared values
Article copyright: © Copyright 1983 American Mathematical Society