Counting rational points on cubic curves

被引：0

作者：

HEATH-BROWN Roger ^{[1
]}

TESTA Damiano ^{[1
]}

机构：

[1] Mathematical Institute,University of Oxford,Oxford,UK

来源：

Science China(Mathematics) | 2010年 / 53卷 / 09期

关键词：

cubic curves; rational points; counting function; elliptic curves; determinant method; m-descent;

D O I：

暂无

中图分类号：

O186.11 [古典微分几何];

学科分类号：

0701 ; 070101 ;

摘要：

We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals.The bounds are uniform in the curve and involve the rank of the corresponding Jacobian.The method used in the proof is a combination of the "determinant method" with an m-descent on the curve.

引用

页码：2259 / 2268

页数：10

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