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

@article{Lee2010HeightBA, title={Height bound and preperiodic points for jointly regular families of rational maps}, author={Chong Gyu Lee}, journal={arXiv: Number Theory}, year={2010} }

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).

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