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＜E-Book＞
Unicity of Meromorphic Mappings / by Pei-Chu Hu, Ping Li, Chung-Chun Yang
(Advances in Complex Analysis and Its Applications ; 1)

Edition	1st ed. 2003.
Publisher	(New York, NY : Springer US : Imprint: Springer)
Year	2003
Language	English
Size	IX, 467 p : online resource
Authors	*Pei-Chu Hu author Ping Li author Chung-Chun Yang author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Functions of complex variables LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Algebraic fields LCSH:Polynomials FREE:Analysis FREE:Several Complex Variables and Analytic Spaces FREE:Functions of a Complex Variable FREE:Global Analysis and Analysis on Manifolds FREE:Field Theory and Polynomials
Notes	1 Nevanlinna theory -- 2 Uniqueness of meromorphic functions on ? -- 3 Uniqueness of meromorphic functions on ?m -- 4 Uniqueness of meromorphic mappings -- 5 Algebroid functions of several variables -- References -- Symbols For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for­ mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func­ tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur­ 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g HTTP:URL=https://doi.org/10.1007/978-1-4757-3775-2

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