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

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

2010-03-16

arxiv.org/abs/1003.3241v2

Mathematics

Number Theory

Scientific paper

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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