Let $K$ be an algebraic field of degree $N$ and let $p$ be an odd prime. It is shown that if $K$ does not contain $p$-th primitive roots of unity and $f(X)=X^{p^k}+c$ with $k\ge1$ and non-zero $c\in K$, then the length of cycles of $f$ in $K$ is bounded by a value depending only on $K$ and $p$. If $p>2^N$, then this bound depends only on $N$.
Publié le : 2010-03-15
Classification:
polynomial cycles,
algebraic number fields.,
11R09,
37C25,
37E15,
37F10
@article{1277811639,
author = {Narkiewicz, W\l adys\l aw},
title = {Cycle-lengths of a class of monic binomials},
journal = {Funct. Approx. Comment. Math.},
volume = {42},
number = {1},
year = {2010},
pages = { 163-168},
language = {en},
url = {http://dml.mathdoc.fr/item/1277811639}
}
Narkiewicz, Władysław. Cycle-lengths of a class of monic binomials. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp. 163-168. http://gdmltest.u-ga.fr/item/1277811639/