Uniqueness of Entire Functions Concerning Differences

doi:10.13371/j.cnki.chin.q.j.m.2021.04.004

Chinese Quarterly Journal of Mathematics ›› 2021, Vol. 36 ›› Issue (4): 376-389.doi: 10.13371/j.cnki.chin.q.j.m.2021.04.004

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Uniqueness of Entire Functions Concerning Differences

Institute of Applied Mathematics, South China Agricultural University

Received:2021-06-01 Online:2021-12-30 Published:2021-12-30
Contact: LIU Dan (1978-), female, native of Wuhan, Hubei, associate professor of South China Agricultural University, Ph. D, engages in complex analysis.
About author: Qiu Shi Lin (1996-), male, native of Shanwei, Guangdong, master candidate of South China Agricultural University, engages in complex analysis; LIU Dan (1978-), female, native of Wuhan, Hubei, associate professor of South China Agricultural University, Ph. D, engages in complex analysis.
Supported by:
Supported by National Natural Science Foundation of China (Grant No. 11701188).

Abstract

Abstract: In this paper, we study the uniqueness of entire functions and prove the following theorem. Let f be a transcendental entire function of finite order. Then there exists at most one positive integer k, such that f ( z )∆ ^k_c f ( z ) −R ( z ) has finitely many zeros, where R ( z ) is a non-vanishing rational function and c is a nonzero complex number. Our result is an improvement of the theorem given by Andasmas and Latreuch [1].

Key words: Nevanlinna theory, Uniqueness, Entire functions, Difference operators

CLC Number:

O174.5

QIU Shi-lin, LIU Dan. Uniqueness of Entire Functions Concerning Differences[J]. Chinese Quarterly Journal of Mathematics, 2021, 36(4): 376-389.

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Uniqueness of Entire Functions Concerning Differences

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