在 20 世纪 60 年代早期，B. Birch 和 H. P. F. Swinnerton-Dyer 推测，如果给定的椭圆曲线有无限多个解，那么相关的 
-级数在某个固定点的值为 0。1976 年，Coates 和 Wiles 证明了具有复数乘法的椭圆曲线如果拥有无限多个解，则其 
-级数在相关的固定点为零（Coates-Wiles 定理），但他们无法证明其逆定理。V. Kolyvagin 将此结果扩展到模曲线。
Swinnerton-Dyer 猜想
另请参阅
Coates-Wiles 定理, 椭圆曲线使用 Wolfram|Alpha 探索
参考文献
Birch, B. and Swinnerton-Dyer, H. "Notes on Elliptic Curves. II." J. reine angew. Math. 218, 79-108, 1965.Cipra, B. "Fermat Prover Points to Next Challenges." Science 271, 1668-1669, 1996.Clay Mathematics Institute. "The Birch and Swinnerton-Dyer Conjecture." http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/.Ireland, K. and Rosen, M. "New Results on the Birch-Swinnerton-Dyer Conjecture." §20.5 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 353-357, 1990.Mazur, B. and Stevens, G. (Eds.). p-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture. Providence, RI: Amer. Math. Soc., 1994.Wiles, A. "The Birch and Swinnerton-Dyer Conjecture." http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/BSD.pdf.引用为
Weisstein, Eric W. "Swinnerton-Dyer 猜想。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/Swinnerton-DyerConjecture.html