| Unicity of Meromorphic Mappings 2003 Edition Contributor(s): Pei-Chu Hu (Author), Ping Li (Author), Chung-Chun Yang (Author) |
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ISBN: 1441952438 ISBN-13: 9781441952431 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: October 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Algebra - General - Mathematics | Functional Analysis |
| Dewey: 515.982 |
| Series: Advances in Complex Analysis and Its Applications |
| Physical Information: 0.97" H x 6.14" W x 9.21" (1.47 lbs) 467 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
