On roots of unity in orbits of rational functions

Alina Ostafe

On roots of unity in orbits of rational functions

Number Theory 2016-05-03 v2

Authors: Alina Ostafe

Abstract

In this paper we characterise univariate rational functions over a number field $\K$ having infinitely many points in the cyclotomic closure $\K^c$ for which the orbit contains a root of unity. Our results are similar to previous results of Dvornicich and Zannier describing all polynomials having infinitely many preperiodic points in $\K^c$ .

Keywords

rational function root of unity orbit number field cyclotomic closure preperiodic point

Cite

@article{arxiv.1603.03983,
  title  = {On roots of unity in orbits of rational functions},
  author = {Alina Ostafe},
  journal= {arXiv preprint arXiv:1603.03983},
  year   = {2016}
}

Comments

The case of of rational functions h=f/g with deg f - deg g<0 has been removed due to a gap in the argument. The main result holds for the case deg f - deg g > 1 only

Related papers

View all related →