Geodesic
Prime rational functions
Omar Kihel 1   ; Jesse Larone 1
1 Department of Mathematics Brock University St. Catharines, Ontario L2S 3A1, Canada
Acta Arithmetica, Tome 169 (2015) no. 1, pp. 29-46 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa169-1-2
Keywords: complex rational function study conditions under which cannot written composition rational functions which units under operation function composition say prime sufficient conditions complex rational functions prime terms their degrees their critical values derive conditions complex polynomials

Omar Kihel  1   ; Jesse Larone  1

1 Department of Mathematics Brock University St. Catharines, Ontario L2S 3A1, Canada 
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Omar Kihel; Jesse Larone. Prime rational functions. Acta Arithmetica, Tome 169 (2015) no. 1, pp. 29-46. doi: 10.4064/aa169-1-2

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