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.

中文翻译：

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多个复变量中亚纯函数的 q 差值分布

在本文中，我们研究了几个复变量值分布理论中几个中心结果的 q 差类似物，例如对数导数引理的 q 差版本、超平面和超曲面的第二个主要定理以及皮卡德类型定理。此外，还获得了关于偏 q 差分多项式的 Tumura-Clunie 定理。最后，我们应用这个理论来研究线性偏 q 差分方程的亚纯解的增长。