论文标题
OGG定理在Weierstrass点上的重量更高
A Higher Weight Analogue of Ogg's Theorem on Weierstrass Points
论文作者
论文摘要
对于一个正整数$ n $，我们说$ \ infty $是模块化曲线上的weierstrass点$ x_0（n）$，如果有非零的浪尖形式的重量$ 2 $ $ 2 $ $γ_0（n）$，它以$ \ infty $的$ \ iffty $消失了，大于$ x_0 $ x_0（n）$ $ x_0 $。如果$ p $是$ p \ nmid n $的素数，则OGG证明$ \ infty $不是$ x_0（pn）$的weierstrass点，如果$ x_0（n）$的属为$ 0 $。我们证明，即使权重$ k \ geq 4 $也是一个类似的结果。我们还研究了重量$ k $ cusp的空间，以$γ_0（n）$消失的订单大于尺寸。
For a positive integer $N$, we say that $\infty$ is a Weierstrass point on the modular curve $X_0(N)$ if there is a non-zero cusp form of weight $2$ on $Γ_0(N)$ which vanishes at $\infty$ to order greater than the genus of $X_0(N)$. If $p$ is a prime with $p \nmid N$, Ogg proved that $\infty $ is not a Weierstrass point on $X_0(pN)$ if the genus of $X_0(N)$ is $0$. We prove a similar result for even weights $k \geq 4$. We also study the space of weight $k$ cusp forms on $Γ_0(N)$ vanishing to order greater than the dimension.
