A Difference Analogue of Cartan’s Second Main Theorem for Meromorphic Mappings

2019 ◽  
Vol 54 (4) ◽  
pp. 240-252
Author(s):  
N. V. Thin
Keyword(s):  
Second Main Theorem ◽  
Meromorphic Mappings ◽  
Difference Analogue

Difference analogues of the second main theorem of zero-order meromorphic mappings for slowly moving targets

2018 ◽  
Vol 11 (04) ◽  
pp. 1850053
Author(s):  
Pham Duc Thoan
Keyword(s):  
Growth Condition ◽  
Zero Order ◽  
Moving Targets ◽  
Second Main Theorem ◽  
Unicity Theorem ◽  
Meromorphic Mappings ◽  
Casorati Determinant ◽  
The Second Main Theorem

In this paper, we show some Second Main Theorems for zero-order meromorphic mappings intersecting slowly moving targets in [Formula: see text] by considering their [Formula: see text]-Casorati determinant. Our results are [Formula: see text]-difference analogues of Cartan’s Second Main Theorem for moving targets. As an application, we give an unicity theorem for meromorphic mappings of [Formula: see text] into [Formula: see text] under the growth condition “order [Formula: see text]”.

Degeneracy second main theorem for meromorphic mappings and moving hypersurfaces with truncated counting functions and applications

2020 ◽  
Vol 31 (06) ◽  
pp. 2050045
Author(s):  
Si Duc Quang
Keyword(s):  
Second Main Theorem ◽  
Algebraic Dependence ◽  
Meromorphic Mappings ◽  
Counting Functions ◽  
The Second Main Theorem

In this paper, we establish a new second main theorem for meromorphic mappings of [Formula: see text] into [Formula: see text] and moving hypersurfaces with truncated counting functions in the case, where the meromorphic mappings may be algebraically degenerate. A version of the second main theorem with weighted counting functions is also given. Our results improve the recent results on this topic. As an application, an algebraic dependence theorem for meromorphic mappings sharing moving hypersurfaces is given.

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