A quantitative estimate for quasi-integral points in orbits

Details A quantitative estimate for quasi-integral points in orbits A quantitative estimate for quasi-integral points in orbits

2009-10-23

arxiv.org/abs/0910.4498v1

Pacific Journal of Math. 249 (2011), 321--342

Mathematics

Number Theory

23 pages

Scientific paper

Let f(z) be a rational function of degree at least 2 with coefficients in a
number field K, and assume that the second iterate f^2(z) of f(z) is not a
polynomial. The second author previously proved that for any b in K, the
forward orbit O_f(b) contains only finitely many quasi-S-integral points. In
this note we give an explicit upper bound for the number of such points.

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