Entire functions that share one value. (English) Zbl 0899.30022

Fang, Mingliang; Hua, Xinhou

J. Nanjing Univ., Math. Biq. 13, No. 1, 44-48 (1996).

The authors prove: Let \(f\) and \(g\) be nonconstant entire functions, \(n> 6\), \(\psi= {f^{(n)} f'-1 \over g^{(n)} g'-1}\). If \(\psi\) and \({1\over\psi}\) are entire functions then \(f^{(n)} f'g^{(n)} g'=1\) or \(f=tg\) with \(t^{n+1} =1\).

Reviewer: A.F.Grishin (Khar’kov)

MSC:

30D35

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Keywords:

sharing value; differential polynomial; Nevanlinna theory; entire functions