zbMATH — the first resource for mathematics

A uniqueness theorem for meromorphic functions whose \(N\)-th derivatives share the same 1-points. (English) Zbl 0799.30019
The authors continue their work on uniqueness theorem arising from common point properties. Their main result here is the theorem: If \(f\) and \(g\) are two meromorphic functions with \(\theta(\infty,f)= \theta(\infty,g)= 1\) and if \(f^{(n)}= 1\) if and only if \(g^{(n)}= 1\) and \(\delta(0,f)+ \delta(0,g)> 1\), then either \(f\equiv q\) or \(f^{(n)} g^{(n)}\equiv 1\).

30D30 Meromorphic functions of one complex variable, general theory
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
Full Text: DOI
[1] H. S. Gopalakrishna and S. S. Bhoosnurmath,Exceptional values of a meromorphic function and its derivatives, Annales Polonici Mathematici35 (1977), 99–105. · Zbl 0371.30026
[2] F. Gross,Factorization of Meromorphic Functions, U. S. Govt. Printing Office Publications, Washington, D.C., 1972. · Zbl 0266.30006
[3] W. K. Hayman,Meromorphic Functions, Oxford University Press, 1964.
[4] M. Ozawa,Unicity theorems for entire functions, J. Analyse Math.30 (1976), 411–420. · Zbl 0337.30020 · doi:10.1007/BF02786728
[5] K. Shibazaki,Unicity theorems for entire functions of finite order. Memoirs of the National Defense Academy, Japan21 (3) (1981), 67–71. · Zbl 0507.30022
[6] C. C. Yang,On two entire functions which together with their first derivatives have the same zeros, J. Math. Anal. Appl.56 (1976), 1–6. · Zbl 0338.30018 · doi:10.1016/0022-247X(76)90002-0
[7] H. X. Yi and C. C. Yang,Unicity theorems for two meromorphic functions with their first derivatives having the same 1 points, Acta Math. Sinica34 (5) (1991), 675–680. · Zbl 0736.30021
[8] Hong-Xun Yi,Meromorphic functions with two deficient values, Acta Math. Sinica30 (5) (1987), 588–597. · Zbl 0654.30023
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.