Iterates of generic polynomials and generic rational functions

Juul, J.

doi:10.1090/tran/7229

Iterates of generic polynomials and generic rational functions

Author: J. Juul
Journal: Trans. Amer. Math. Soc. 371 (2019), 809-831
MSC (2010): Primary 37P05; Secondary 11G35, 14G25, 12F10
DOI: https://doi.org/10.1090/tran/7229
Published electronically: April 25, 2018
MathSciNet review: 3885162
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Abstract: In 1985, Odoni showed that in characteristic 0 the Galois group of the -th iterate of the generic polynomial with degree is as large as possible. That is, he showed that this Galois group is the -th wreath power of the symmetric group . We generalize this result to positive characteristic, as well as to the generic rational function. These results can be applied to prove certain density results in number theory, two of which are presented here. This work was partially completed by the late R.W.K. Odoni in an unpublished paper.

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