A quantitative estimate for quasiintegral points in orbits

Liang Chung Hsia; Joseph H. Silverman

doi:10.2140/pjm.2011.249.321

A quantitative estimate for quasiintegral points in orbits

Liang Chung Hsia^*, Joseph H. Silverman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 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	https://doi.org/10.2140/pjm.2011.249.321
Publication status	Published - 2011
Externally published	Yes

Keywords

Arithmetic dynamics
Integral points

ASJC Scopus subject areas

General Mathematics

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10.2140/pjm.2011.249.321

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title = "A quantitative estimate for quasiintegral points in orbits",

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",

author = "Hsia, {Liang Chung} and Silverman, {Joseph H.}",

year = "2011",

doi = "10.2140/pjm.2011.249.321",

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AU - Silverman, Joseph H.

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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

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DO - 10.2140/pjm.2011.249.321

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JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

A quantitative estimate for quasiintegral points in orbits

Abstract

Keywords

ASJC Scopus subject areas

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