Unicity of Meromorphic Mappings (Advances in Complex Analysis and Its Applications)

Pei-Chu Hu; Ping Li; Chung-Chun Yang

ISBN 10: 1402012195 / ISBN 13: 9781402012198

Verlag: Kluwer, Dordrecht, 2003

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No markings. Bestandsnummer des Verkäufers 00038022

Bibliografische Details

Titel: Unicity of Meromorphic Mappings (Advances in...

Verlag: Kluwer, Dordrecht

Erscheinungsdatum: 2003

Einband: Hardcover

Zustand: Fine

Auflage: First Edition.

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Book by PeiChu Hu Ping Li ChungChun Yang

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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.