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Second main theorems with weighted counting functions and algebraic dependence of meromorphic mappings


Author: Si Duc Quang
Journal: Proc. Amer. Math. Soc. 144 (2016), 4329-4340
MSC (2010): Primary 32H30, 32A22; Secondary 30D35
Published electronically: April 13, 2016
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Abstract: The purpose of this article is twofold. The first is to prove a new second main theorem for meromorphic mappings and moving hyperplanes of $ \mathbb{P}^n(\mathbb{C})$, where the counting functions are truncated multiplicities and have different weights. Our result is an extension of previous second main theorems for moving hyperplanes with the truncated (to level $ n$) counting functions. As its application, the second purpose of this article is to prove a new algebraic dependence theorem for meromorphic mappings having the same inverse images of some moving hyperplanes, where the moving hyperplanes involve the assumption with different roles.


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Additional Information

Si Duc Quang
Affiliation: Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy, Cau Giay, Hanoi, Vietnam
Email: quangsd@hnue.edu.vn

DOI: https://doi.org/10.1090/proc/13061
Keywords: Nevanlinna, second main theorem, meromorphic mapping, moving hyperplane
Received by editor(s): December 5, 2015
Published electronically: April 13, 2016
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society