English

Preperiodic points for rational functions defined over a rational function field of characteristic zero

Number Theory 2015-08-28 v2 Dynamical Systems

Abstract

Let kk be an algebraic closed field of characteristic zero. Let KK be the rational function field K=k(t)K=k(t). Let ϕ\phi be a non isotrivial rational function in K(z)K(z). We prove a bound for the cardinality of the set of KK--rational preperiodic points for ϕ\phi in terms of the number of places of bad reduction and the degree dd of ϕ\phi.

Keywords

Cite

@article{arxiv.1505.07753,
  title  = {Preperiodic points for rational functions defined over a rational function field of characteristic zero},
  author = {J. K. Canci},
  journal= {arXiv preprint arXiv:1505.07753},
  year   = {2015}
}

Comments

There was a mistake in the previous version. The results have been proven only for rational function fields

R2 v1 2026-06-22T09:43:16.038Z