Visualising modular forms

Goal:

Modular forms are analytic functions on the upper half plane of the complex plane satisfying certain simple transformations and/or symmetries. They play a prominent role in number theory.

In this project, modular forms shall be visualised. For instance, plots like those on the wikipedia page of Klein's j-invariant shall be produced for other modular forms. Optionally, one could also think about 3D-plots of modular forms.

Schedule: To be determined.

Supervisors: Gabor Wiese, Panagiotis Tsaknias.

Difficulty level: Introductory/Medium.

Tools: Computer algebra systems like Sage, possibly some graphics software.

Results: [too be completed at the end of the project.]

FSCT -- University of Luxembourg