Value distribution and uniqueness on \(q\)-differences of meromorphic functions (Q2843789)
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scientific article; zbMATH DE number 6201379
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Value distribution and uniqueness on \(q\)-differences of meromorphic functions |
scientific article; zbMATH DE number 6201379 |
Statements
26 August 2013
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uniqueness
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\(q\)-difference polynomial
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characteristic function
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sharing value
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Value distribution and uniqueness on \(q\)-differences of meromorphic functions (English)
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The author considers the value distribution of some \(q\)-difference polynomial of a meromorphic function \(f\) of order zero. Let \(q\) be a nonzero complex constant and \(P\) a nonconstant polynomial of degree \(n\). Denote by \(m\) the number of distinct roots of \(P(z)=0\). It is shown that if \(n>2m+3\) then \(P(f(z))f(qz)-a(z)\) has infinitely many zeros for any small function \(a\) with respect to \(f\). The author also considers a uniqueness problem for meromorphic functions of order zero using Nevanlinna theory.
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