Proof of a conjecture of Gross concerning fix-points (Q1823336)
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scientific article; zbMATH DE number 4114958
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proof of a conjecture of Gross concerning fix-points |
scientific article; zbMATH DE number 4114958 |
Statements
Proof of a conjecture of Gross concerning fix-points (English)
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1990
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It is proved that if f and g are transcendental entire functions and if Q is a non-constant polynomial, then the equation \(f(g(z))=Q(z)\) has infinitely many solutions. In particular, f(g(z)) has an infinite number of fix-points. This confirms a conjecture of \textit{F. Gross} [Factorization of meromorphic functions (1972; Zbl 0266.30006)].
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prime function
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Wiman-Valiron theory
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entire functions
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fix-points
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factorization
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