Meromorphic functions sharing three values with their shift
UDC 517.5 We discuss the  problem of uniqueness of a meromorphic function $f(z),$ which shares $a_1(z)$, $a_2(z),$ and $a_3(z)$ CM with its shift $f(z+c)$, where $a_1(z)$, $a_2(z),$ and $a_3(z)$ are three $c$-periodic distinct small functions of $f(z)$ and $c\i...
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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7502 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.5
We discuss the  problem of uniqueness of a meromorphic function $f(z),$ which shares $a_1(z)$, $a_2(z),$ and $a_3(z)$ CM with its shift $f(z+c)$, where $a_1(z)$, $a_2(z),$ and $a_3(z)$ are three $c$-periodic distinct small functions of $f(z)$ and $c\in\mathbb{C}\setminus\{0\}$. The obtained result improves the recent result of Heittokangas et al. [Complex Var. and Elliptic Equat., 56, No. 1–4, 81–92 (2011)]  by dropping the assumption about the order of $f(z)$.  In addition, we introduce a way of characterizing elliptic functions in terms of meromorphic functions  sharing values with two of their shifts.  Moreover, we show by  a number of illustrating examples that  our results are,  in certain senses, best possible. |
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| DOI: | 10.3842/umzh.v76i5.7502 |