Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917568702316544 |
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| author | Huang, XiaoHuang |
| author_facet | Huang, XiaoHuang |
| contents | In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let $f$ be a non-constant meromorphic function satisfying $ρ_{2}(f)<1$, let $η$ be a non-zero complex number, and let $a,b,c\in\hat{S}(f)$ be three distinct small functions. If $f$ and $Δ^{n}_ηf$ share $a,b,c$ CM, then $f\equiv Δ^{n}_ηf$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_08958 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators Huang, XiaoHuang Complex Variables 30D35 In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let $f$ be a non-constant meromorphic function satisfying $ρ_{2}(f)<1$, let $η$ be a non-zero complex number, and let $a,b,c\in\hat{S}(f)$ be three distinct small functions. If $f$ and $Δ^{n}_ηf$ share $a,b,c$ CM, then $f\equiv Δ^{n}_ηf$. |
| title | Unicity on meromorphic function sharing three small functions CM with its higher-order difference operators |
| topic | Complex Variables 30D35 |
| url | https://arxiv.org/abs/2106.08958 |