Download Unicity of Meromorphic Mappings (Advances in Complex by Pei-Chu Hu,Ping Li,Chung-Chun Yang PDF

By Pei-Chu Hu,Ping Li,Chung-Chun Yang

For a given meromorphic functionality I(z) and an arbitrary worth a, Nevanlinna's price distribution concept, which are derived from the well-known Poisson-Jensen for­ mula, offers with relationships among the expansion of the functionality and quantitative estimations of the roots of the equation: 1 (z) - a = O. within the Twenties as an program of the distinguished Nevanlinna's worth distribution concept of meromorphic capabilities, R. Nevanlinna [188] himself proved that for 2 nonconstant meromorphic func­ tions I, nine and 5 certain values ai (i = 1,2,3,4,5) within the prolonged aircraft, 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 four, then 1 = L(g), the place L denotes an appropriate Mobius transformation. Then within the 19708, F. Gross and C. C. Yang began to examine the same yet extra basic questions of 2 services that proportion units of values. for example, they proved that if 1 and nine are nonconstant whole capabilities and eight , eighty two and eighty three are 3 specific finite units such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.

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