Vol. 249, No. 2, 2011

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A quantitative estimate for quasiintegral points in orbits

Liang-Chung Hsia and Joseph H. Silverman

Vol. 249 (2011), No. 2, 321–342
Abstract

Let φ(z) K(z) be a rational function of degree d 2 defined over a number field whose second iterate φ2(z) is not a polynomial, and let α K. The second author previously proved that the forward orbit 𝒪φ(α) contains only finitely many quasi-S-integral points. We give an explicit upper bound for the number of such points.

Keywords
arithmetic dynamics, integral points
Mathematical Subject Classification 2010
Primary: 37P15
Secondary: 11B37, 11G99, 14G99
Milestones
Received: 22 October 2009
Accepted: 8 December 2009
Published: 1 February 2011
Authors
Liang-Chung Hsia
Department of Mathematics
National Central University
Chung-Li 32054
Taiwan
Joseph H. Silverman
Department of Mathematics, Box 1917
Brown University
151 Thayer Street
Providence, RI 02912
United States
http://www.math.brown.edu/~jhs