Integral points on a certain family of elliptic curves

被引：4

作者：

Akhtari, Shabnam ^{[1
]}

机构：

[1] Univ Oregon, Eugene, OR 97403 USA

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2015年 / 27卷 / 02期

关键词：

Elliptic Curvers; Quartic Thue equations;

D O I：

10.5802/jtnb.905

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Thue-Siegel method is used to obtain an upper bound for the number of primitive integral solutions to a family of quartic Thue's inequalities. This will provide an upper bound for the number of integer points on a family of elliptic curves with j-invariant equal to 1728.

引用

页码：353 / 373

页数：21

共 16 条

[1] AKHTARI S., REPRESENTAT IN PRESS
[2] The method of Thue-Siegel for binary quartic forms
Akhtari, Shabnam
[J]. ACTA ARITHMETICA, 2010, 141 (01) : 1 - 31
[3] ON THUES EQUATION
BOMBIERI, E
SCHMIDT, WM
[J]. INVENTIONES MATHEMATICAE, 1987, 88 (01) : 69 - 81
[4] ON THE METHOD OF THUE-SIEGEL
CHUDNOVSKY, GV
[J]. ANNALS OF MATHEMATICS, 1983, 117 (02) : 325 - 382
[5] CREMONA J. E., 1999, LMS J COMPUT MATH, V2, P62
[6] UNIFORM BOUNDS FOR THE NUMBER OF SOLUTIONS TO YN=F(X)
EVERTSE, JH
SILVERMAN, JH
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1986, 100 : 237 - 248
[7] Integral points on elliptic curves and 3-torsion in class groups
Helfgott, H. A.
Venkatesh, A.
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 19 (03) : 527 - 550
[8] Lenstra Jr H.W., 2002, Not. Am. Math. Soc., V49, P182
[9] LEWIS D. J., 1969, MAA STUDIES MATH, P6
[10] MORDELL L. J., 1969, Diophantine equations

← 1 2 →