On the functional equation f(p(z))=g(q(z)), where p,q are "generalized" polynomials and f,g are meromorphic functions

The functional equation f(p(z))=g(q(z)) is studied, where p,q are polynomials and f,g are trancendental meromorphic functions in C. We find all the pairs p,q for which there exist nonconstant f,g satisfying our equation and there exist no rational f,g with this property. In fact, a more general prob...

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Bibliographic Details
Published inarXiv.org
Main Author Lysenko, Sergei
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.06.1996
Subjects
Functional equations
Mathematical analysis
Meromorphic functions
Polynomials
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Summary:The functional equation f(p(z))=g(q(z)) is studied, where p,q are polynomials and f,g are trancendental meromorphic functions in C. We find all the pairs p,q for which there exist nonconstant f,g satisfying our equation and there exist no rational f,g with this property. In fact, a more general problem is solved. In addition to algebraic methods, some results from local analytic dynamics are used.
ISSN:2331-8422
DOI:10.48550/arxiv.9606217