论文标题
椭圆曲线的分析等级
Analytic ranks of elliptic curves over number fields
论文作者
论文摘要
令$ e $为$ \ mathbb {q} $的椭圆曲线。然后，我们表明，超过$ \ $ \ mathbb {q} $的$ l $ $ e $的平均分析等级，$ l $ a $ a Prime不等于$ 2 $，最多是$ 2+r _ {\ mathbb {q}}}（q}}}（e）$，其中$ r _ {超过$ \ mathbb {q} $。该界限独立于学位$ l $，我们还获得了超过$ s_d $ fields的一些平均分析等级结果。
Let $E$ be an elliptic curve over $\mathbb{Q}$. Then, we show that the average analytic rank of $E$ over cyclic extensions of degree $l$ over $\mathbb{Q}$ with $l$ a prime not equal to $2$, is at most $2+r_{\mathbb{Q}}(E)$, where $r_{\mathbb{Q}}(E)$ is the analytic rank of the elliptic curve $E$ over $\mathbb{Q}$. This bound is independent of the degree $l$ Also, we also obtain some average analytic rank results over $S_d$-fields.
