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Books > Science & Mathematics > Mathematics > Algebra
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Unicity of Meromorphic Mappings (Paperback, 2003)
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Unicity of Meromorphic Mappings (Paperback, 2003)
Series: Advances in Complex Analysis and Its Applications, 1
Expected to ship within 18 - 22 working days
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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.
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