Prime and composite Laurent polynomials

2007/10/22 by F. Pakovich, Pakovich, F. · 2 citations
Mathematics · #14H30 #30F99 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14H30 #msc:30F99

paper · pdf · doi:10.48550/arxiv.0710.3860

Some of the proofs given in sections 6-8 are simplified. Some other small alterations were made

arxiv created 2008/12/31 · arxiv updated 2009/12/01

Abstract

In 1922 Ritt constructed the theory of functional decompositions of polynomials with complex coefficients. In particular, he described explicitly indecomposable polynomial solutions of the functional equation f(p(z))=g(q(z)). In this paper we study the equation above in the case when f,g,p,q are holomorphic functions on compact Riemann surfaces. We also construct a self-contained theory of functional decompositions of rational functions with at most two poles generalizing the Ritt theory. In particular, we give new proofs of the theorems of Ritt and of the theorem of Bilu and Tichy.

Cited by

• Monodromy groups of polynomials of composition length 2
• Periodic curves for general endomorphisms of \mathbb C\mathbb P¹× \mathbb C\mathbb P¹

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