Mock heegner points and congruent numbers
Mock heegner points and congruent numbers
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DOI：
10.1007/bf02570859
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发表时间：
1990-12
影响因子：
0.8
通讯作者：
P. Monsky
中科院分区：
文献类型：
--
作者：
P. Monsky
设N是无平方因子的正整数，E（NI）是由NV 2= U3-U定义的椭圆曲线.很容易看出E~（1）的扭子群是Z/2 × Z/2，如果E~（1）有正秩，或者更具体地说，如果存在有理u和v，v. 0，且NvZ= u ~ 3-u，我们称N是”全等数”。决定哪些N是全等数以及找到最后一个方程的解的问题是一个古老的问题-其历史见[5]，最近的结果见[6]。
Let N be a square-free positive integer and E (NI be the elliptic curve defined by NV 2= U 3-U. It's easily seen that the torsion subgroup of E~~) is Z/2 x Z/2; we say that N is a" congruent number" if E~) has positive rank, or more concretely if there exist rational u and v, v. 0 with NvZ= u3-u. The problem of deciding which N are congruent numbers and of finding solutions to this last equation is an old one-for its history see [5] and for recent results see