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Prime rational functions

Volume 169 / 2015

Omar Kihel, Jesse Larone Acta Arithmetica 169 (2015), 29-46 MSC: Primary 11C08; Secondary 12E05, 26C15. DOI: 10.4064/aa169-1-2

Abstract

Let $f(x)$ be a complex rational function. We study conditions under which $f(x)$ cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that $f(x)$ is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we also derive some conditions for the case of complex polynomials.

Authors

  • Omar KihelDepartment of Mathematics
    Brock University
    St. Catharines, Ontario L2S 3A1, Canada
    e-mail
  • Jesse LaroneDepartment of Mathematics
    Brock University
    St. Catharines, Ontario L2S 3A1, Canada
    e-mail

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