非同余子群上模形式的计算

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2023-10-30 DOI:10.1090/mcom/3903
David Berghaus, Hartmut Monien, Danylo Radchenko
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引用次数: 1

摘要

我们提出了两种可用于计算非同余子群上模形式的方法。第一种方法使用了Hejhal的方法,我们改进了任意精度求解技术,使算法在实际计算中速度提高了两个数量级。这使我们能够获得傅立叶系数的高精度数值估计,从中可以使用LLL算法识别代数表达式。第二种方法被限制为零属子群,并使用有效的方法来计算Belyi映射,从Belyi映射可以构造模形式。
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On the computation of modular forms on noncongruence subgroups
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.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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