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2021 | OriginalPaper | Chapter

Visualizing Modular Forms

Author : David Lowry-Duda

Published in: Arithmetic Geometry, Number Theory, and Computation

Publisher: Springer International Publishing

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Abstract

The chapter 'Visualizing Modular Forms' delves into the intricacies of plotting complex functions, with a focus on modular forms. It begins by discussing the motivation and challenges of visualizing complex functions, which naturally form surfaces in four dimensions. The authors explore various techniques, including domain coloring and phase plotting, and emphasize the use of colormaps from Python’s matplotlib library to enhance visual perception. The chapter provides a detailed survey of existing complex plotting methods, including those by Farris and Wegert, and demonstrates their application to modular forms. Through practical examples and comparisons, the authors highlight the distinctive features and behaviors of different modular forms, offering insights into their symmetries and cusps. The chapter concludes with recommendations for producing effective visualizations, making it a valuable resource for professionals and researchers in the field of mathematical visualization.
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Metadata
Title
Visualizing Modular Forms
Author
David Lowry-Duda
Copyright Year
2021
Book
Arithmetic Geometry, Number Theory, and Computation

Print ISBN: 978-3-030-80913-3

Electronic ISBN: 978-3-030-80914-0

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-80914-0_19

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