How to implement a modular form

被引：2

作者：

Raum, Martin ^{[1
]}

机构：

[1] MPI Math, D-53111 Bonn, Germany

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2011年 / 46卷 / 12期

关键词：

Modular forms; Fourier expansions; Computation; COMPUTATIONS;

D O I：

10.1016/j.jsc.2011.08.013

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We present a model for Fourier expansions of arbitrary modular forms. This model takes precisions and symmetries of such Fourier expansions into account. The value of this approach is illustrated by studying a series of examples. An implementation of these ideas is provided by the author. We discuss the technical background of this implementation, and we explain how to implement arbitrary Fourier expansions and modular forms. The framework allows us to focus on the considerations of a mathematical nature during this procedure. We conclude with a list of currently available implementations and a discussion of possible computational research. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1336 / 1354

页数：19

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