On the equation P(f)=Q(g), where P,Q are polynomials and f,g are entire functions

2008/04/04 by Fedor Pakovich, F. Pakovich, Pakovich, F.
Mathematics · #30D05 #39B32 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #math.CV #msc:30D05 #msc:39B32

paper · pdf · doi:10.48550/arxiv.0804.0739

Final version, to appear in Amer. Journal of Math

openalex publication_date 2008/04/04 · arxiv created 2009/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1922 Ritt described polynomial solutions of the functional equation P(f)=Q(g). In this paper we describe solutions of the equation above in the case when P,Q are polynomials while f,g are allowed to be arbitrary entire functions. In fact, we describe solutions of the more general functional equation s=P(f)=Q(g), where s,f,g are entire functions and P,Q are arbitrary rational functions. Besides, we solve the problem of description of "strong uniqueness polynomials" for entire functions.

Citations

• Decompositions of Laurent polynomials

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