SECOND MAIN THEOREM AND UNIQUENESS PROBLEM OF ZERO-ORDER MEROMORPHIC MAPPINGS FOR HYPERPLANES IN SUBGENERAL POSITION

• Luong, Thi Tuyet (Department of Mathematics National University of Civil Engineering) ;
• Nguyen, Dang Tuyen (Department of Mathematics National University of Civil Engineering) ;
• Pham, Duc Thoan (Department of Mathematics National University of Civil Engineering)
• Accepted : 2017.08.11
• Published : 2018.01.31

Abstract

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

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