Prime and composite Laurent polynomials TeX Export

@misc{citeulike:1810474, abstract = {In 1922 Ritt constructed a factorization theory for polynomials with respect to the composition operation and described explicitly polynomial solutions of the functional equation \$f(p(z))=g(q(z)).\$ In this paper we construct a self-contained factorization theory for rational functions with at most two poles. In particular, we give new proofs of the theorems of Ritt and of the theorem of Bilu and Tishy. Besides, we study general properties of the equation above in the case when \$f,g,p,q\$ are holomorphic functions on compact Riemann surfaces.}, archivePrefix = {arXiv}, author = {Pakovich, F.}, citeulike-article-id = {1810474}, citeulike-linkout-0 = {http://arxiv.org/abs/0710.3860}, citeulike-linkout-1 = {http://arxiv.org/pdf/0710.3860}, eprint = {0710.3860}, keywords = {complex\_analysis, univariate\_functions}, month = {Oct}, posted-at = {2007-10-23 13:02:12}, priority = {4}, title = {Prime and composite Laurent polynomials}, url = {http://arxiv.org/abs/0710.3860}, year = {2007} }

TY - ELEC ID - citeulike:1810474 L3 - citeulike-article-id:1810474 N2 - In 1922 Ritt constructed a factorization theory for polynomials with respect to the composition operation and described explicitly polynomial solutions of the functional equation $f(p(z))=g(q(z)).$ In this paper we construct a self-contained factorization theory for rational functions with at most two poles. In particular, we give new proofs of the theorems of Ritt and of the theorem of Bilu and Tishy. Besides, we study general properties of the equation above in the case when $f,g,p,q$ are holomorphic functions on compact Riemann surfaces. TI - Prime and composite Laurent polynomials KW - complex_analysis KW - univariate_functions AU - Pakovich, F PY - 2007/Oct/22/ UR - http://arxiv.org/abs/0710.3860 ER -