Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one
Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one
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证明解析阶零和一的特定椭圆曲线的 Birch 和 Swinnerton-Dyer 猜想
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发表时间：
2010
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通讯作者：
Robert L. Miller
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作者：
Robert L. Miller
对任意给定的解析秩为0或1的有理数上定义的椭圆曲线，给出了证明Birch和Swinnerton-Dyer猜想公式的一种算法。在计算机辅助下，我们证明了16725条导体小于5000的此类曲线中的16714条的公式。
We describe an algorithm to prove the Birch and Swinnerton-Dyer conjectural formula for any given elliptic curve defined over the rational numbers of analytic rank zero or one. With computer assistance we have proved the formula for 16714 of the 16725 such curves of conductor less than 5000.