论文标题
加权堆栈形态图像的高度界点，用于计算椭圆曲线的应用
Points of bounded height in images of morphisms of weighted projective stacks with applications to counting elliptic curves
论文作者
论文摘要
给出了加权投影堆栈形态的理性点数量的渐近点，其图像的高度有界限并满足一组（可能是无限）的局部条件。结果，我们获得了在具有规定级别结构的数字字段上计数椭圆曲线的结果，其中包括$ n \ in \ in \ {1,2,3,4,5 \} $ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ in \ {1,2，\ dots，$ n \ $ n \ $ n \ $ n \ $γ（n）$的情况（\ dots $ n \ dots $ n \ dots $ n） $ n \ in \ {1,2,4,6,8,9,12,16,18 \} $。在所有情况下，我们都会给出带有领先系数的表达式的渐近学，在许多情况下，我们还提供了节省功率的误差项。
Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results for counting elliptic curves over number fields with prescribed level structures, including the cases of $Γ(N)$ for $N\in\{1,2,3,4,5\}$, $Γ_1(N)$ for $N\in\{1,2,\dots,10,12\}$, and $Γ_0(N)$ for $N\in\{1,2,4,6,8,9,12,16,18\}$. In all cases we give an asymptotic with an expression for the leading coefficient, and in many cases we also give a power-saving error term.
