Hiroshima Mathematical Journal

On unicity of meromorphic functions when two differential polynomials share one value

Chao Meng

Full-text: Open access

Abstract

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following result: Let $f$ and $g$ be two nonconstant meromorphic functions and let $n(\geq 14)$ be an integer such that $n+1$ is not divisible by $3$. If $f^{n}(f^{3}-1)f'$ and $g^{n}(g^{3}-1)g'$ share $(1,2)$ or $``(1,2)"$, then $f\equiv g$. If $\overline{E}_{4)}(1,f^{n}(f^{3}-1)f')=\overline{E}_{4)}(1,g^{n}(g^{3}-1)g')$ and $E_{2)}(1,f^{n}(f^{3}-1)f')=E_{2)}(1,g^{n}(g^{3}-1)g')$, then $f\equiv g$.

Article information

Source
Hiroshima Math. J., Volume 39, Number 2 (2009), 163-179.

Dates
First available in Project Euclid: 31 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1249046335

Digital Object Identifier
doi:10.32917/hmj/1249046335

Mathematical Reviews number (MathSciNet)
MR2543648

Zentralblatt MATH identifier
1182.30051

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory

Keywords
Uniqueness meromorphic function differential polynomials

Citation

Meng, Chao. On unicity of meromorphic functions when two differential polynomials share one value. Hiroshima Math. J. 39 (2009), no. 2, 163--179. doi:10.32917/hmj/1249046335. https://projecteuclid.org/euclid.hmj/1249046335


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