Integer points on elliptic curves

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)237-252
Number of pages16
JournalPacific Journal of Mathematics
Volume222
Issue number2
DOIs
Publication statusPublished - 2005 Dec

Fingerprint

Integer Points
Gross
Number field
Elliptic Curves
Division
Exponent
Unit
Language

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Integer points on elliptic curves. / Chi, Wen Chen; Lai, King Fai; Tan, K. I.Seng.

In: Pacific Journal of Mathematics, Vol. 222, No. 2, 12.2005, p. 237-252.

Research output: Contribution to journalArticle

Chi, Wen Chen ; Lai, King Fai ; Tan, K. I.Seng. / Integer points on elliptic curves. In: Pacific Journal of Mathematics. 2005 ; Vol. 222, No. 2. pp. 237-252.
@article{0a0327d5c7294071b28104aebccc5d95,
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 = "12",
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",
number = "2",

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=32344441141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=32344441141&partnerID=8YFLogxK

U2 - 10.2140/pjm.2005.222.237

DO - 10.2140/pjm.2005.222.237

M3 - Article

AN - SCOPUS:32344441141

VL - 222

SP - 237

EP - 252

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -