论文标题
椭圆曲线和班级数的下限
Elliptic curves and lower bounds for class numbers
论文作者
论文摘要
理想的班级配对将等级的理性点$ r \ geq 1 $椭圆曲线$ e/\ q $与理想的类群$ \ cl（-d）$的某些想象二次段落的$。这些配对意味着 $ h（-d）\ geq \ frac {1} {2}（c（e） - \ varepsilon）（\ log d）^{\ frac {r} {r} {2}} $$，用于在某些家庭中有足够大的大歧视$ -D $，其中某些家庭中的$ c（e）是自然常量的。这些界限是有效的，它们为许多判别物提供了已知的下限的改进。
Ideal class pairings map the rational points of rank $r\geq 1$ elliptic curves $E/\Q$ to the ideal class groups $\CL(-D)$ of certain imaginary quadratic fields. These pairings imply that $$h(-D) \geq \frac{1}{2}(c(E)-\varepsilon)(\log D)^{\frac{r}{2}} $$ for sufficiently large discriminants $-D$ in certain families, where $c(E)$ is a natural constant. These bounds are effective, and they offer improvements to known lower bounds for many discriminants.
