论文标题
在$ x_0（n）$上的高阶Weierstrass点上
On Higher Order Weierstrass Points on $X_0(N)$
论文作者
论文摘要
令$γ$为第一类的紫红色群体。对于均匀的整数$ m \ ge 4 $，我们描述了$ h^{m/2} \ left（\ mathfrakr_γ\右）的$ m/2 $ - holomorphic差异差异，以子空间$ s_m^h（γ）$（Holomorphic）cuspidal模式$ s_m s_m（γ）这将经典的同构$ s_2（γ）\ simeq h^{1} \ left（\ mathfrakr_γ\ right）$。我们研究$ s_m^h（γ）$的属性。作为一个应用程序，我们描述了在SAGE中实现的算法，用于测试是否为$ \ indperelliptic $ x_0（n）$的$ \ infty $是$ \ frac {m} {2} {2} $ - weierstrass点。
Let $Γ$ be the Fuchsian group of the first kind. For an even integer $m\ge 4$, we describe the space $H^{m/2}\left(\mathfrak R_Γ\right)$ of $m/2$--holomorphic differentials in terms of a subspace $S_m^H(Γ)$ of the space of (holomorphic) cuspidal modular forms $S_m(Γ)$. This generalizes classical isomorphism $S_2(Γ)\simeq H^{1}\left(\mathfrak R_Γ\right)$. We study the properties of $S_m^H(Γ)$. As an application, we describe the algorithm implemented in SAGE for testing if a cusp at $\infty$ for non-hyperelliptic $X_0(N)$ is a $\frac{m}{2}$-Weierstrass point.
