Bulletin of the Belgian Mathematical Society - Simon Stevin

Unicity of meromorphic functions related to their derivatives

Qi Han and Pei-Chu Hu

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Abstract

In this paper, we shall study the unicity of meromorphic functions defined over non-Archimedean fields of characteristic zero such that their valence functions of poles grow slower than their characteristic functions. If $f$ is such a function, and $f$ and a linear differential polynomial $P(f)$ of $f$, whose coefficients are meromorphic functions growing slower than $f$, share one finite value $a$ CM, and share another finite value $b\ (\not=a)$ IM, then $P(f)=f$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 5 (2007), 905-918.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1197908902

Mathematical Reviews number (MathSciNet)
MR2378996

Zentralblatt MATH identifier
1181.30018

Subjects
Primary: 12J25: Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
Secondary: 46S10: Functional analysis over fields other than $R$ or $C$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]

Keywords
uniqueness of meromorphic functions value sharing Nevanlinna theory non-Archimedean analysis

Citation

Han, Qi; Hu, Pei-Chu. Unicity of meromorphic functions related to their derivatives. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 5, 905--918. https://projecteuclid.org/euclid.bbms/1197908902


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