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

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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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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Jiangxi, 330031, China

    T.-B. Cao

  2. Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101, Joensuu, Finland

    R. J. Korhonen

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  1. T.-B. Cao
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  2. R. J. Korhonen
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Correspondence to R. J. Korhonen.

Additional information

The first author was supported by the National Natural Science Foundation of China (#11871260, #11461042), and the outstanding young talent assistance program of Jiangxi Province (#20171BCB23002) in China.

The second author was supported in part by the Academy of Finland grant (#286877).

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Cao, TB., Korhonen, R.J. Value distribution of q-differences of meromorphic functions in several complex variables. Anal Math 46, 699–736 (2020). https://doi.org/10.1007/s10476-020-0058-2

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  • DOI: https://doi.org/10.1007/s10476-020-0058-2

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