Computational Methods and Function Theory

, Volume 17, Issue 4, pp 613–634 | Cite as

Uniqueness Theorems for Differential Polynomials Sharing a Small Function

  • Thi Hoai An TaEmail author
  • Viet Phuong Nguyen


Consider meromorphic functions fg,  and \(\alpha ,\) where \(\alpha \) is a small function with respect to f and g. Let Q be a polynomial of one variable. We give suitable conditions on the degree of Q and on the number of zeros and the multiplicities of the zeros of \(Q'\) so as to be able to conclude uniqueness results if differential polynomials of the form \((Q(f))^{(k)}\) and \((Q(g))^{(k)}\) share \(\alpha \) counting multiplicities. We do not assume that Q has a large order zero, nor do we place restrictions on the zeros and poles of \(\alpha .\) Thus, our work improves on many prior results that either assume Q has a high order zero or place restrictions on the small function \(\alpha \).


Meromorphic functions Entire functions Nevanlinna theory Uniqueness Sharing value Differential polynomial 

Mathematics Subject Classification




We would like to thank the referees for useful suggestions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  2. 2.Institute of Mathematics and Applied Sciences (TIMAS)Thang Long UniversityHanoiVietnam
  3. 3.Thai Nguyen University of Economics and Business AdministrationThai NguyenVietnam

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