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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Bibliographic Details
Published in:Analysis mathematica (Budapest) Vol. 46; no. 4; pp. 699 - 736
Main Authors: Cao, T.-B., Korhonen, R. J.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2020
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-020-0058-2