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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rational functions with linear relations


Authors: Ariane M. Masuda and Michael E. Zieve
Journal: Proc. Amer. Math. Soc. 136 (2008), 1403-1408
MSC (2000): Primary 39B12; Secondary 12E05, 30D05
Published electronically: December 7, 2007
MathSciNet review: 2367113
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Abstract | References | Similar Articles | Additional Information

Abstract: We find all polynomials $ f,g,h$ over a field $ K$ such that $ g$ and $ h$ are linear and $ f(g(x))=h(f(x))$. We also solve the same problem for rational functions $ f,g,h$, in case the field $ K$ is algebraically closed.


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Additional Information

Ariane M. Masuda
Affiliation: School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada
Address at time of publication: Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 5B6, Canada
Email: amasuda@uottawa.ca

Michael E. Zieve
Affiliation: Center for Communications Research, 805 Bunn Drive, Princeton, New Jersey 08540
Email: zieve@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09246-5
PII: S 0002-9939(07)09246-5
Keywords: Functional equation, commuting rational functions
Received by editor(s): February 15, 2007
Published electronically: December 7, 2007
Additional Notes: The authors thank Bob Beals, Alan Beardon, Alex Erëmenko, and Patrick Ng for useful correspondence.
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.