论文信息 - A quantitative estimate for quasi-integral points in orbits

A quantitative estimate for quasi-integral points in orbits

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.

J. Silverman | Liang-Chung Hsia

[1] J. Silverman. Height Estimates for Equidimensional Dominant Rational Maps , 2009, 0908.3835.

[2] Joseph H. Silverman,et al. Primitive divisors in arithmetic dynamics , 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

[3] Joseph H. Silverman,et al. A Local-Global Criterion for Dynamics on P^1 , 2008 .

[4] J. Silverman. The Arithmetic of Dynamical Systems , 2007 .

[5] Joseph H. Silverman,et al. Diophantine Geometry: An Introduction , 2000 .

[6] J. Silverman,et al. S-INTEGER POINTS ON ELLIPTIC CURVES , 1995 .

[7] Nigel P. Smart,et al. S-integral points on elliptic curves , 1994, Mathematical Proceedings of the Cambridge Philosophical Society.

[8] Joseph H. Silverman,et al. Integer points, Diophantine approximation, and iteration of rational maps , 1993 .

[9] R. Gross. A note on Roth's Theorem , 1990 .

[10] Joseph H. Silverman,et al. Arithmetic distance functions and height functions in diophantine geometry , 1987 .

[11] Joseph H. Silverman,et al. A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves. , 1987 .

[12] K. Zsigmondy,et al. Zur Theorie der Potenzreste , 1892 .