Author | Hu, Pei-Chu. author |
---|---|

Title | Unicity of Meromorphic Mappings [electronic resource] / by Pei-Chu Hu, Ping Li, Chung-Chun Yang |

Imprint | Boston, MA : Springer US : Imprint: Springer, 2003 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-3775-2 |

Descript | IX, 467 p. online resource |

SUMMARY

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 forยญ 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 funcยญ 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. Furยญ 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

CONTENT

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

Mathematics
Algebra
Field theory (Physics)
Mathematical analysis
Analysis (Mathematics)
Functions of complex variables
Global analysis (Mathematics)
Manifolds (Mathematics)
Mathematics
Analysis
Several Complex Variables and Analytic Spaces
Functions of a Complex Variable
Global Analysis and Analysis on Manifolds
Field Theory and Polynomials