论文标题
在galois cm场上模块化椭圆曲线的比例下限
A lower bound on the proportion of modular elliptic curves over Galois CM fields
论文作者
论文摘要
我们计算出在任何不包含$ζ_5$的galois cm字段上模块化的椭圆曲线比例的显式下限。应用于虚构的二次字段，此比例至少为$ 2/5 $。适用于Cyclotomic字段$ \ Mathbb {Q}（ζ_N）$，$ 5 \ nmid n $，此比例至少为$ 1- \ varepsilon $，只有$ n $有限的除外，对于$ \ varepsilon> 0 $ 0 $。
We calculate an explicit lower bound on the proportion of elliptic curves that are modular over any Galois CM field not containing $ζ_5$. Applied to imaginary quadratic fields, this proportion is at least $2/5$. Applied to cyclotomic fields $\mathbb{Q}(ζ_n)$ with $5\nmid n$, this proportion is at least $1-\varepsilon$ with only finitely many exceptions of $n$, for any choice of $\varepsilon > 0$.
