Composite rational functions having a bounded number of zeros and poles
Clemens Fuchs, Attila Pethő · Proceedings of the American Mathematical Society · 2010
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.