论文标题
关于椭圆曲线分析等级的分布
On the distribution of analytic ranks of elliptic curves
论文作者
论文摘要
在本文中，根据GRH的椭圆形$ L $ functions，我们为具有分析等级的椭圆曲线的概率提供了上限，$ a \ geq 11 $，也给出了$ n $ th $ n $ th的上限。这些是将椭圆曲线计算为本地条件的应用，例如，在$ p $中降低了良好的减少。
In this paper, under GRH for elliptic $L$-functions, we give an upper bound for the probability for an elliptic curve with analytic rank $\leq a$ for $a \geq 11$, and also give an upper bound of $n$-th moments of analytic ranks of elliptic curves. These are applications of counting elliptic curves with local conditions, for example, having good reduction at $p$.
