Prime and composite Laurent polynomials

By F. Pakovich. 2007

62 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2a02a5a2f74192fd707a5d5d44e8df29cf6747c0

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In Applied Mathematics

1. Colin Christopher
2. A. Álvarez
3. J. Bravo

In Geometry and Topology

1. Colin Christopher
2. A. Álvarez
3. J. Bravo

Citations in the corpus

• Classification of flexible Kokotsakis polyhedra with quadrangular base (2014, unknown): “1 Branched covers, elliptic curves, and Euler–Chasles correspondences Another example of an application of complex analysis to an algebraic problem is Ritt’s characterization of composite and commutative polynomials [16, 18].”
• ON RITT'S POLYNOMIAL DECOMPOSITION THEOREMS (2008, unknown): “A G ] 2 3 Ju l 2 00 8”
• On the trigonometric moment problem (2011, background): “For more details see [16] or [23, Lemma 2.”