Integer points on elliptic curves

Wen Chen Chi; King Fai Lai; K. I.Seng Tan

doi:10.2140/pjm.2005.222.237

Integer points on elliptic curves

Wen Chen Chi^*, King Fai Lai, K. I.Seng Tan

^*Corresponding author for this work

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We study Lang's conjecture on the number of S-integer points on an elliptic curve over a number field. We improve the exponent of the bound of Gross and Silverman from quadratic to linear by using the S-unit equation method of Evertse and a formula on 2-division points.

Original language	English
Pages (from-to)	237-252
Number of pages	16
Journal	Pacific Journal of Mathematics
Volume	222
Issue number	2
DOIs	https://doi.org/10.2140/pjm.2005.222.237
Publication status	Published - 2005 Dec

Keywords

2-division points
Elliptic curves
Integer points
Lang's conjecture
S-integers
S-unit equations

ASJC Scopus subject areas

General Mathematics

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10.2140/pjm.2005.222.237

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title = "Integer points on elliptic curves",

abstract = "We study Lang's conjecture on the number of S-integer points on an elliptic curve over a number field. We improve the exponent of the bound of Gross and Silverman from quadratic to linear by using the S-unit equation method of Evertse and a formula on 2-division points.",

keywords = "2-division points, Elliptic curves, Integer points, Lang's conjecture, S-integers, S-unit equations",

author = "Chi, {Wen Chen} and Lai, {King Fai} and Tan, {K. I.Seng}",

year = "2005",

month = dec,

doi = "10.2140/pjm.2005.222.237",

language = "English",

volume = "222",

pages = "237--252",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California, Berkeley",

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T1 - Integer points on elliptic curves

AU - Chi, Wen Chen

AU - Lai, King Fai

AU - Tan, K. I.Seng

PY - 2005/12

Y1 - 2005/12

N2 - We study Lang's conjecture on the number of S-integer points on an elliptic curve over a number field. We improve the exponent of the bound of Gross and Silverman from quadratic to linear by using the S-unit equation method of Evertse and a formula on 2-division points.

AB - We study Lang's conjecture on the number of S-integer points on an elliptic curve over a number field. We improve the exponent of the bound of Gross and Silverman from quadratic to linear by using the S-unit equation method of Evertse and a formula on 2-division points.

KW - 2-division points

KW - Elliptic curves

KW - Integer points

KW - Lang's conjecture

KW - S-integers

KW - S-unit equations

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DO - 10.2140/pjm.2005.222.237

M3 - Article

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VL - 222

SP - 237

EP - 252

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

Integer points on elliptic curves

Abstract

Keywords

ASJC Scopus subject areas

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