Counting rational points on cubic curves

Counting rational points on cubic curves

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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. 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.

作者 HEATH-BROWN Roger TESTA Damiano

机构地区 Mathematical Institute

出处《Science China Mathematics》 SCIE 2010年第9期2259-2268,共10页 中国科学：数学（英文版）

关键词 CUBIC CURVES rational points COUNTING function ELLIPTIC CURVES DETERMINANT method m-descent cubic curves rational points counting function elliptic curves determinant method m-descent

分类号 O186.11 [理学—基础数学]

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Science China Mathematics

2010年第9期

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Counting rational points on cubic curves

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