English

Height bound and preperiodic points for jointly regular families of rational maps

Number Theory 2010-04-27 v2

Abstract

Silverman proved a height inequality for jointly regular family of rational maps and the author improved it for jointly regular pairs. In this paper, we provide the same improvement for jointly regular family; if S is a jointly regular set of rational maps, then \sum_{f\in S} \dfrac{1}{\deg f} h\bigl(f(P) \bigr) > (1+ \dfrac{1}{r}) f(P) - C where r = \max_{f\in S} r(f).

Keywords

Cite

@article{arxiv.1003.3241,
  title  = {Height bound and preperiodic points for jointly regular families of rational maps},
  author = {ChongGyu Lee},
  journal= {arXiv preprint arXiv:1003.3241},
  year   = {2010}
}