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.
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页码：2259 / 2268
页数：10
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