Prime and composite Laurent polynomials

Details Prime and composite Laurent polynomials Prime and composite Laurent polynomials

2007-10-22

arxiv.org/abs/0710.3860v5

Mathematics

Complex Variables

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

Scientific paper

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.

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