SOME RESULTS ON COMPLEX DIFFERENTIAL-DIFFERENCE ANALOGUE OF BRÜCK CONJECTURE

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, a...

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Veröffentlicht in:	Communications of the Korean Mathematical Society 2017, Vol.32 (2), p.361-373
Hauptverfasser:	Chen, Min Feng, Gao, Zong Sheng
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description	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 $f(z+{\eta})-f(z){\not\equiv}0$.
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title	SOME RESULTS ON COMPLEX DIFFERENTIAL-DIFFERENCE ANALOGUE OF BRÜCK CONJECTURE
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