论文标题
关于非综合子组的模块化形式的计算
On the computation of modular forms on noncongruence subgroups
论文作者
论文摘要
我们提出了两种可用于计算非统一亚组模块化形式的方法。第一种方法使用Hejhal的方法，我们改善了任意精确求解技术，以使算法在实际计算中最多更快。这使我们能够获得可以使用LLL算法识别代数表达式的傅立叶系数的高精度数值估计。第二种方法仅限于零子组属，并使用有效的方法来计算可以从中构建模块化形式的Belyi映射。
We present two approaches that can be used to compute modular forms on noncongruence subgroups. The first approach uses Hejhal's method for which we improve the arbitrary precision solving techniques so that the algorithm becomes about up to two orders of magnitude faster in practical computations. This allows us to obtain high precision numerical estimates of the Fourier coefficients from which the algebraic expressions can be identified using the LLL algorithm. The second approach is restricted to genus zero subgroups and uses efficient methods to compute the Belyi map from which the modular forms can be constructed.
