Prime and composite Laurent polynomials

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27 Scopus citations

Abstract

In the paper [J. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc. 23 (1922) 51-66] Ritt constructed the theory of functional decompositions of polynomials with complex coefficients. In particular, he described explicitly polynomial solutions of the functional equation f (p (z)) = g (q (z)). In this paper we study the equation above in the case where 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.

Original languageEnglish
Pages (from-to)693-732
Number of pages40
JournalBulletin des Sciences Mathematiques
Volume133
Issue number7
DOIs
StatePublished - 1 Oct 2009

Keywords

  • Decompositions of Laurent polynomials
  • Decompositions of rational functions
  • Ritt's theorems

ASJC Scopus subject areas

  • General Mathematics

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