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arXiv · 2106.08958

Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators

XiaoHuang Huang
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Abstract

In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let $f$ be a non-constant meromorphic function satisfying $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number, and let $a,b,c\in\hat{S}(f)$ be three distinct small functions. If $f$ and $\Delta^{n}_{\eta}f$ share $a,b,c$ CM, then $f\equiv \Delta^{n}_{\eta}f$.

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XiaoHuang Huang. 2021-05-10. Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators. https://arxiv.org/abs/2106.08958

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