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http://dx.doi.org/10.4134/CKMS.c160123

SOME RESULTS ON COMPLEX DIFFERENTIAL-DIFFERENCE ANALOGUE OF BRÜCK CONJECTURE  

Chen, Min Feng (LMIB and School of Mathematics and Systems Science Beihang University)
Gao, Zong Sheng (LMIB and School of Mathematics and Systems Science Beihang University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.2, 2017 , pp. 361-373 More about this Journal
Abstract
In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of $Br{\ddot{u}}ck$ conjecture. In other words, we consider ${\Delta}_{\eta}f(z)=f(z+{\eta})-f(z)$ and f'(z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where ${\eta}{\in}{\mathbb{C}}{\backslash}\{0\}$ is a constant such that $f(z+{\eta})-f(z){\not\equiv}0$.
Keywords
Nevanlinna theory; uniqueness theory; $Br{\ddot{u}}ck$ conjecture; differential-difference equation;
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Times Cited By KSCI : 1  (Citation Analysis)
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