For a positive integer N, we say that ∞ is a Weierstrass point on the modular curve X0(N) if there is a non-zero cusp form of weight 2 on Γ0(N) which vanishes at ∞ to order greater than the genus of X0(N). If p is a prime with p ∤ N, Ogg proved that ∞ is not a Weierstrass point on X0(pN) if the genus of X0(N) is 0. We prove a similar result for even weights k ≥ 4. We also study the space of weight k cusp forms on Γ0(N) vanishing to order greater than the dimension.

中文翻译：

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Ogg 定理在 Weierstrass 点上的更高权重类似物

对于一个正整数ñ, 我们说∞是模曲线上的 Weierstrass 点X0(ñ)如果有一个非零尖头形式的重量2在Γ0(ñ)消失在∞订购大于的属X0(ñ). 如果p是一个素数p ∤ ñ, 奥格证明了∞不是魏尔斯特拉斯点X0(pñ)如果属X0(ñ)是0. 我们证明了偶数权重的类似结果ķ ≥ 4. 我们还研究了重量空间ķ尖头形式Γ0(ñ)消失的顺序大于维度。