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arXiv · 1612.07416

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

Tingbin Cao·Risto Korhonen
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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.

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Tingbin Cao, Risto Korhonen. 2020-11-21. Value distribution of q-differences of meromorphic functions in several complex variables. https://doi.org/10.1007/s10476-020-0058-2

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