Weierstrass points at irregular cusps

Abstract

In this paper, we prove that all irregular cusps on $X_1(N)$ of genus $\ge 2$ are Weierstrass points except for $X_1(18)$. Also, for any positive integer $N$ of the form $p^{2}M$ with a prime $p$ and a positive integer $M$, we obtain some results for when the irregular cusps of $X_0(N)$ equivalent to $\left(\begin{array}{c}1\\ p\end{array}\right)$ are Weierstrass points or not.

9 pages

References in corpus (1)

• On the arithmetic of certain modular curves