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Unicity of meromorphic functions related to their derivatives. (English) Zbl 1181.30018

Summary: 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 \(b (\neq a)\) IM, then \(P(f)=f\).

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
12J25 Non-Archimedean valued fields
30G06 Non-Archimedean function theory
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
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Full Text: Euclid