Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.11.20
  • Accepted : 2017.08.11
  • Published : 2018.01.31
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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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References

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