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Iterates of Generic Polynomials and Gene...
Juul, Jamie...

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Iterates of Generic Polynomials and Generic Rational Functions by Juul, Jamie ( Author )
Lemonjar Open Access
Australian National University
06-09-2023
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 This work was partially completed by the late R.W.K. Odoni in an unpublished paper.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1410.3814
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