A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables

2016/01/21 by Tingbin Cao, Risto Korhonen, Cao, Tingbin +1 · 6 citations
Mathematics · #Meromorphic and Entire Functions #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1601.05716

Abstract

Let c∈ ℂ^m, f:ℂ^m→ℙⁿ(ℂ) be a linearly nondegenerate meromorphic mapping over the field P_c of c-periodic meromorphic functions in ℂ^m, and let H_j (1≤ j≤ q) be q(>2N-n+1) hyperplanes in N-subgeneral position of ℙⁿ(ℂ). We prove a new version of the second main theorem for meromorphic mappings of hyperorder strictly less than one without truncated multiplicity by considering the Casorati determinant of f instead of its Wronskian determinant. As its applications, we obtain a defect relation, a uniqueness theorem and a difference analogue of generalized Picard theorem.

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