Prime and composite Laurent polynomials☆ Export

@article{citeulike:5347705, 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.}, author = {Pakovich, F.}, citeulike-article-id = {5347705}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.bulsci.2009.06.003}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0007449709000372}, day = {26}, doi = {10.1016/j.bulsci.2009.06.003}, issn = {00074497}, journal = {Bulletin des Sciences Math\'{e}matiques}, keywords = {commutative\_algebra, complex\_analysis, geometric\_combinatorics, univariate\_functions}, month = {June}, posted-at = {2009-10-28 07:33:26}, priority = {4}, title = {Prime and composite Laurent polynomials☆}, url = {http://dx.doi.org/10.1016/j.bulsci.2009.06.003}, year = {2009} }

TY - JOUR ID - citeulike:5347705 L3 - citeulike-article-id:5347705 N2 - 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. JF - Bulletin des Sciences Mathématiques SN - 00074497 TI - Prime and composite Laurent polynomials☆ KW - commutative_algebra KW - complex_analysis KW - geometric_combinatorics KW - univariate_functions AU - Pakovich, F PY - 2009/06/26/ UR - http://dx.doi.org/10.1016/j.bulsci.2009.06.003 ER -