### Abstract

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

Original language | English |
---|---|

Pages (from-to) | 321-342 |

Number of pages | 22 |

Journal | Pacific Journal of Mathematics |

Volume | 249 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 Feb 15 |

### Fingerprint

### Keywords

- Arithmetic dynamics
- Integral points

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*249*(2), 321-342. https://doi.org/10.2140/pjm.2011.249.321

**A quantitative estimate for quasiintegral points in orbits.** / Hsia, Liang Chung; Silverman, Joseph H.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 249, no. 2, pp. 321-342. https://doi.org/10.2140/pjm.2011.249.321

}

TY - JOUR

T1 - A quantitative estimate for quasiintegral points in orbits

AU - Hsia, Liang Chung

AU - Silverman, Joseph H.

PY - 2011/2/15

Y1 - 2011/2/15

N2 - 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.

AB - 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.

KW - Arithmetic dynamics

KW - Integral points

UR - http://www.scopus.com/inward/record.url?scp=79851497656&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79851497656&partnerID=8YFLogxK

U2 - 10.2140/pjm.2011.249.321

DO - 10.2140/pjm.2011.249.321

M3 - Article

AN - SCOPUS:79851497656

VL - 249

SP - 321

EP - 342

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -