Composite rational functions having a bounded number of Zeros and Poles

Clemens Fuchs, Attila Petho

Research output: Contribution to journalArticle

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)31-38
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number1
Publication statusPublished - Jan 1 2011


  • Brownawell-Masser inequality
  • Decomposability
  • Lacunarity
  • Mason-Stothers inequality
  • Rational functions
  • Siegel's identity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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