论文标题
关于二次曲折的数量，高度几乎最小
On the number of quadratic twists with a rational point of almost minimal height
论文作者
论文摘要
我们研究了给定椭圆曲线的二次曲折家族中具有几乎最小高度的合理点的曲线数量。这个问题起源于Hooley的工作，Hooley在实际二次领域的情况下问了这个问题。特别是，他对几乎最小的基本单位的此类领域的数量显示了渐近估计。我们的主要结果在固定椭圆曲线的二次曲折的环境中建立了模拟渐近公式。
We investigate the number of curves having a rational point of almost minimal height in the family of quadratic twists of a given elliptic curve. This problem takes its origin in the work of Hooley, who asked this question in the setting of real quadratic fields. In particular, he showed an asymptotic estimate for the number of such fields with almost minimal fundamental unit. Our main result establishes the analogue asymptotic formula in the setting of quadratic twists of a fixed elliptic curve.
