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Entire Functions and their Derivatives Share Two Finite Sets

Fang, Ming Liang, (2001) Entire Functions and their Derivatives Share Two Finite Sets. Bulletin of the Malaysian Mathematical Sciences Society, 24 (1). pp. 7-16. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v24n1/v24n1p2.pdf

Affiliations

Nanjing Normal University, Dept. of Mathematics
Southeast University, State Key Laboratory of Millimeter Waves

Abstract

In this paper, we study the uniqueness of entire functions. We mainly obtain the following result: Let $ f(z) $ and $ g(z) $ be two non-constant entire functions. $ n \geq 5 $, $ k $ two positive integers, and let $ S_1 = \{ z:z^n = 1 \} $, $ S_2 = \{ a,b,c \} $ where $ a, b, c $ are nonzero finite distinct constants satisfying $ a^2 \neq bc, b^2 \neq ac, c^2 \neq ab $ . If $ E(S_1 , f) = E(S_1 , g) , E(S_2 , f^{(k)}) = E(S_2 , g^{(k)}) $, then $ f(z) \equiv g(z)$.

Item Type:Journal
Keywords:Entire function, derivative, uniqueness, finite set
Subjects:Q Science, Computer Science
ID Code:1325

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