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Composite rational functions having a bounded number of zeros and poles


Authors: Clemens Fuchs and Attila Pethő
Journal: Proc. Amer. Math. Soc. 139 (2011), 31-38
MSC (2010): Primary 11R58; Secondary 14H05, 12Y05
DOI: https://doi.org/10.1090/S0002-9939-2010-10684-6
Published electronically: September 1, 2010
MathSciNet review: 2729068
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study composite rational functions which have at most a given number of distinct zeros and poles. A complete algorithmic characterization of all such functions and decompositions is given. This can be seen as a multiplicative analog of a result due to Zannier on polynomials that are lacunary in the sense that they have a bounded number of non-constant terms.


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Additional Information

Clemens Fuchs
Affiliation: Department of Mathematics, ETH Zurich, Rämistrasse 101, 8092 Zürich, Switzerland
Email: clemens.fuchs@math.ethz.ch

Attila Pethő
Affiliation: Department of Computer Science, University of Debrecen, Number Theory Research Group, Hungarian Academy of Sciences and University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary
Email: petho.attila@inf.unideb.hu

DOI: https://doi.org/10.1090/S0002-9939-2010-10684-6
Keywords: Rational functions, decomposability, lacunarity, Siegel’s identity, Mason-Stothers inequality, Brownawell-Masser inequality
Received by editor(s): January 21, 2010
Published electronically: September 1, 2010
Additional Notes: The second author’s research was supported in part by the Hungarian National Foundation for Scientific Research grant No. T67580.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2010 American Mathematical Society

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