A Difference Picard Theorem for Meromorphic Functions of Several Variables
By R. Korhonen. 2009
63 citations recorded by the source corpus.
It is shown that if n ∈ ℕ, c ∈ ℂn, and three distinct values of a meromorphic function f: ℂn sr 1 of hyper-order gV(f) strictly less than 2/3 have forward invariant pre-images with respect to a translation τ: ℂn sr ℂn, τ (z) = z + c, then f is a periodic function with period c. This result can be seen as a generalization of M. Green’s Picard-Type Theorem in the special case where gV(f) < 2/3, since the empty pre-images of the usual Picard exceptional values are by definition always forward invariant. In addition, difference analogues of the Lemma on the Logarithmic Derivative and of the Second Main Theorem of Nevanlinna theory for meromorphic functions ℂn → ℙ P1 are given, and their applications to partial difference equations are discussed.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d18e437ad4b3991d26cea493037db4a6122db326
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables (2016, methodology): “In [7] a difference analogue of the lemma on the logarithmic derivatives was obtained for meromorphic functions in several variables of hyperorder strictly less that 2/3.”