Value distribution of q-differences of meromorphic functions in several complex variables

In this paper, we study q -difference analogues of several central results in value distribution theory of several complex variables such as q -difference versions of the logarithmic derivative lemma, the second main theorem for hyperplanes and hypersurfaces, and a Picard type theorem. Moreover, the...

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Vydané v:Analysis mathematica (Budapest) Ročník 46; číslo 4; s. 699 - 736
Hlavní autori: Cao, T.-B., Korhonen, R. J.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.12.2020
Predmet:
Analysis
Mathematics
Mathematics and Statistics
difference equation
primary 32H30
Picard type theorem
logarithmic derivative lemma
secondary 30D35, 39A14
second main theorem
Tumura-Clunie theorem
partial
ISSN:0133-3852, 1588-273X
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Abstract In this paper, we study q -difference analogues of several central results in value distribution theory of several complex variables such as q -difference versions of the logarithmic derivative lemma, the second main theorem for hyperplanes and hypersurfaces, and a Picard type theorem. Moreover, the Tumura–Clunie theorem concerning partial q -difference polynomials is also obtained. Finally, we apply this theory to investigate the growth of meromorphic solutions of linear partial q -difference equations.
AbstractList In this paper, we study q -difference analogues of several central results in value distribution theory of several complex variables such as q -difference versions of the logarithmic derivative lemma, the second main theorem for hyperplanes and hypersurfaces, and a Picard type theorem. Moreover, the Tumura–Clunie theorem concerning partial q -difference polynomials is also obtained. Finally, we apply this theory to investigate the growth of meromorphic solutions of linear partial q -difference equations.
Author Korhonen, R. J.
Cao, T.-B.
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  surname: Korhonen
  fullname: Korhonen, R. J.
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  organization: Department of Physics and Mathematics, University of Eastern Finland
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Issue 4
Keywords difference equation
primary 32H30
Picard type theorem
logarithmic derivative lemma
secondary 30D35, 39A14
second main theorem
Tumura-Clunie theorem
partial
Language English
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PublicationTitle Analysis mathematica (Budapest)
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Snippet In this paper, we study q -difference analogues of several central results in value distribution theory of several complex variables such as q -difference...
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SubjectTerms Analysis
Mathematics
Mathematics and Statistics
Title Value distribution of q-differences of meromorphic functions in several complex variables
URI https://link.springer.com/article/10.1007/s10476-020-0058-2
Volume 46
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