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Transactions of the American Mathematical Society

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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 $ n$-th iterate of the generic polynomial with degree $ d$ is as large as possible. That is, he showed that this Galois group is the $ n$-th wreath power of the symmetric group $ S_d$. 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 This work was partially completed by the late R.W.K. Odoni in an unpublished paper.


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Additional Information

J. Juul
Affiliation: Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts 01002
Email: jamie.l.rahr@gmail.com

DOI: https://doi.org/10.1090/tran/7229
Received by editor(s): May 13, 2015
Received by editor(s) in revised form: March 16, 2016, and January 22, 2017
Published electronically: April 25, 2018
Additional Notes: This work was partially supported by NSF grant DMS-1200749
Dedicated: Dedicated to R.W.K. Odoni
Article copyright: © Copyright 2018 American Mathematical Society