SOLUTIONS OF THE CUBIC FERMAT EQUATION IN QUADRATIC FIELDS

被引：2

作者：

Jones, Marvin ^{[1
]}

Rouse, Jeremy ^{[2
]}

机构：

[1] Univ S Carolina, Dept Math, Columbia, SC 29208 USA

[2] Wake Forest Univ, Dept Math, Winston Salem, NC 27109 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2013年 / 9卷 / 06期

关键词：

Elliptic curve; Fermat equation; modular form; half-integer weight modular form; Waldspurger's theorem; MODULAR-FORMS; ELLIPTIC-CURVES; DERIVATIVES; POINTS;

D O I：

10.1142/S1793042113500449

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give necessary and sufficient conditions on a squarefree integer d for there to be non-trivial solutions to x(3) + y(3) = z(3) in Q(root d), conditional on the Birch and Swinnerton-Dyer conjecture. These conditions are similar to those obtained by J. Tunnell in his solution to the congruent number problem.

引用

页码：1579 / 1591

页数：13

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