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MATHEMATICS
On the type of the meromorphic function of finite order
M. V. Kabanko Kursk State University, ul. Radishcheva, 33, Kursk,
305000, Russia
Abstract:
Let f(z) be a meromorphic function on the complex plane of finite order ρ>0. Let ρ(r) be a proximate order in the sense of Boutroux such that lim supr→∞ρ(r)=ρ, lim infr→∞ρ(r)=α>0. If [α]<α⩽ρ<[α]+1 then the types of T(r,f) and |N|(r,f) coincide with respect to ρ(r). If there are integers between α and ρ, 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.
Received: 14.11.2022 Accepted: 29.05.2023
Citation:
M. V. Kabanko, “On the type of the meromorphic function of finite order”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:2 (2023), 212–224
Linking options:
https://www.mathnet.ru/eng/vuu845 https://www.mathnet.ru/eng/vuu/v33/i2/p212
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Abstract page: | 233 | Full-text PDF : | 68 | References: | 55 |
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