论文标题
尖峰形式的计算动作
Computing actions on cusp forms
论文作者
论文摘要
对于正整数$ k $和$ n $，我们描述了如何计算$ sl_2（\ mathbb {z}）$在cusp forms forms $ s_k（γ（n））$上的自然动作，其中cusp形式通过其$ q $ expexpansion提供了足够多的术语。这将减少计算Atkin-Lehner运算符对$ s_k（γ）$的动作，用于一致性子组$γ_1（n）\subseteqγ\subseteqγ_0（n）$。我们激励这种基本计算的激励应用是计算某些模块化曲线的明确模型$ x_g $。
For positive integers $k$ and $N$, we describe how to compute the natural action of $SL_2(\mathbb{Z})$ on the space of cusp forms $S_k(Γ(N))$, where a cusp form is given by sufficiently many terms of its $q$-expansion. This will reduce to computing the action of the Atkin--Lehner operator on $S_k(Γ)$ for a congruence subgroup $Γ_1(N)\subseteq Γ\subseteq Γ_0(N)$. Our motivating application of such fundamental computations is to compute explicit models of some modular curves $X_G$.
