On the asymptotic values of meromorphic functions in the $n$-fold punctured plane
UDC 517.5 We present some results  on the asymptotic paths and asymptotic values for meromorphic functions in the $n$-fold extended punctured plane $\widehat{\mathbb{C}}\backslash\{p_{1},\ldots,p_{n}\} .$ These results extend some classical results obtained for...
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| Дата: | 2025 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2025
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7882 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.5
We present some results  on the asymptotic paths and asymptotic values for meromorphic functions in the $n$-fold extended punctured plane $\widehat{\mathbb{C}}\backslash\{p_{1},\ldots,p_{n}\} .$ These results extend some classical results obtained for analytic and meromorphic functions in the complex plane $\mathbb{C}.$  In particular, in this more general setting,  we give a version of   F. Iversen's result on the existence of asymptotic values for entire functions  in the plane.  We also obtain a bound for the number of isolated directly critical singularities of a meromorphic function of finite order $k$ and a finite number of poles. |
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| DOI: | 10.3842/umzh.v76i11.7882 |