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Russia Kursk
Year
2023
Volume
33
Issue
2
Pages
212-224
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Section Mathematics
Title On the type of the meromorphic function of finite order
Author(-s) Kabanko M.V.a
Affiliations Kursk State Universitya
Abstract Let $f(z)$ be a meromorphic function on the complex plane of finite order $\rho>0$. Let $\rho(r)$ be a proximate order in the sense of Boutroux such that $\limsup\limits_{r\to\infty}\rho(r)=\rho$, $\liminf\limits_{r\to\infty}\rho(r)=\alpha>0$. If $[\alpha]<\alpha\leqslant\rho<[\alpha]+1$ then the types of $T(r,f)$ and $|N|(r,f)$ coincide with respect to $\rho(r)$. If there are integers between $\alpha$ and $\rho$, then the resulting criterion is formulated in terms of the upper density of zeros and poles of the function $f$ and their argument symmetry.
Keywords meromorphic function, function order, function type, upper density, argument symmetry
UDC 517.53
MSC 30D35, 30D30, 42A16, 30D15
DOI 10.35634/vm230202
Received 14 November 2022
Language Russian
Citation Kabanko M.V. On the type of the meromorphic function of finite order, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 2, pp. 212-224.
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